The impact of working slope angleson the open-pit mining economics

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Authors Upadhyay, Raja Prasad, 1944-

Publisher The University of Arizona.

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THE IMPACT OF WORKING SLOPE ANGLES ON THE OPEN-PIT MINING ECONOMICS

byRaja Prasad Upadhyay

A Thesis Submitted to the Faculty of theDEPARTMENT OF MINING AND GEOLOGICAL ENGINEERINGIn Partial Fulfillment of the Requirements

For the Degree ofMASTER OF SCIENCE

WITH A MAJOR IN MINING ENGINEERINGIn the Graduate College

THE UNIVERSITY OF ARIZONA

19 7 5

STATEMENT BY AUTHOR

This thesis has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made, available to borrowers under rules of the Library.

Brief quotations from this thesis are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major depart­ment or the Dean of the Graduate College when in his judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author.

SIGNED:

APPROVAL BY THESIS DIRECTOR This thesis has been approved on the date shown below:

/ J T . Z / / J Y. C. Kim : ~ W Date7

Associate Professor of Mining and Geological Engineering

ACKNOWLEDGMENTS

The work presented in this thesis was conducted under the supervision of Dr. Young C, Kim, Associate Professor of Mining and Geological Engineering. The author wishes to express his gratitude to Dr. Kim for his valuable supervision and guidance.

The interest and invaluable suggestions of Dr. Thomas J. O’Neil and Dr. Richard D. Call of Mining and Geological Engineering are also gratefully acknowledged.

Finally, Canadian Department of Energy, Mines and Resources, is to be thanked for the financial support.

TABLE OF CONTENTS

PageLIST OF TABLES . . . . . . . . . . . . . . . . . . viLIST OF ILLUSTRATIONS . .viiiABSTRACT . . . . > . . . . . . . . . . . . . . . . ix

I. INTRODUCTION . . .... . ........... 1Statement of the Problem ................... 3Review of the Related Studies. . . . . . . . . 4

II. OPEN-PIT MINE PLANNING AND ECONOMICS.......... 6Ultimate Pit Slope Angle ........... 6Working Slope Angle. . . . . . . . . . . . . . 7Pre-Production Stripping ....... 9Mining Sequence............. . 12

III. MODEL FORMULATION. . . . . . . . . . . . . . . . . 13A Benefit Cost Model . . . . . . . . . . . . . 16

Sectors in the Pit ..........16Probabilities of Failures........... 17Type and Frequency of Failures . . . . . . 18Sampling of the Pit Wall Failure . . . . . 18Mining Costs . . . . . . . . . . . . . . . 24Cost of Failure. ........... . . . . . 24Model Assumption . . . . . . . . . . . . . 25Computer Program . . . . . . . . . . . . . 2 6

Financial Risk Analysis Model. . . . . . . . . 27Risk Analysis. . 27Monte-Carlo Sampling . . . . . . . . . . . 28

- Decision Criteria. . . . . . . . . . . . . 28Probability Distribution . . . . . . . . . 30Cash Flow Computation. . . . . . . . . . . 3 2Model Assumptions. . . . . . . . . . . . . 34Computer Program . . . . . . . . . . . . . 34

IV. MODEL TESTING. . . . . . . . . . . . . . 36Testing of Benefit Cost Model. . . . . . . . . 37

Assumptions. . .............. . . . . 37Discussion of the Results......... 38

iv

VTABLE OF CONTENTS, Continued

PageTesting of Financial Risk AnalysisModel. . . ......... . . . . . . . . . . . 48Discussion of the Results. . ........... 48

CONCLUSION AND RECOMMENDATIONS . ............... 54Conclusions. . ........... . . . . . . . . 54Recommendations. . . . . . . . . . . . . . . . 55

APPENDIX A: NOTES ON COST OF FAILURE........... 57APPENDIX B: THE BENEFIT COST MODEL COMPUTER

PROGRAM . . . . . . . . . . 62APPENDIX C: INPUT DATA AND OUTPUTS OF THE

BENEFIT COST MODEL. . . . . . . . . . 79APPENDIX D: FINANCIAL RISK ANALYSIS

COMPUTER PROGRAM......... 92APPENDIX E: INPUT DATA AND OUTPUTS OF THE

FINANCIAL RISK ANALYSIS MODEL . . . . 112SELECTED BIBLIOGRAPHY 132

LIST OF TABLES

Table Page1. Cash Flow Computation..................... . 332. Annual Incremental Benefits for

Working Slope Angle of 25° . 393. Annual Incremental Benefits for Working

Slope Angle of 35°. ......... 404. Annual Incremental Costs of Working

Slope Angle of 25°. . . . . . . . . . . . . . . . . 415. Annual Incremental Costs of Working

Slope Angle of 35°. . . . . . . ... . . . . . . . . 426. Sensitivity Analysis of Clean-up Cost on

the Incremental Net Present Values of 35°Slope Over 25° Slope (At Standard Probabilityof Failure Values)............. 44

7. Sensitivity Analysis of Clean-up Cost on the Incremental Net Present Values of 35° Slope Over 25° Slope (At 25% Increased Probabilityof Failure) . ... . . . . . . . . . . . . . . . . . . 45

8. Sensitivity Analysis of Probability of Failure on the Incremental Net Present Values of 35° Slope Over 25° Slope (Clean-up Cost at 1.25 times the UnitMining Cost). . . . . . . . . . . . . . . . . . . .46

9. Sensitivity Analysis of Probability of Failure on the Incremental Net Present Values of 35° Slope Over 25° Slope (Clean-up Cost at3.00 Times the Unit Mining Cost)................47

10. Intermediate Results Showing Annual Cash Flows and Associated NPV, DCFROI, WGR for Each SlopeAngle Discount Factor Used = 15%. . . . . . . . . . 49

11. Sorted Values of Increased NPV, DCFROI and WGRfor 35° Working Slope Compared to 25° ........... 50

Vll

LIST OF TABLES, Continued

Table Page12. The Results Obtained by the Four

Different Runs of the Financial RiskAnalysis. Model. 52

LIST OF ILLUSTRATIONS

Figure Page1. Working Slope in Single.Bench Pattern . . . . . . 82. Working Slope in Multi-Bench Pattern......... 83. Pre-production Stripping for Two

Different Types of Ore Bodies............. 114. Schematic of the Pit Slope Economics Model. . . . 145. Geometry of the Pit in Different

Stages of-Mining............. 206. Geometry of the Pit in Case of Push-Back. . . . . 217. Geometry of the Pit Wall in Case of

Kink in the Slope . . . . ......... 23

viii

ABSTRACT

A pit slope economics model is developed to analyze the economic impact of steepening the working slope angle in an open-pit mining operation. The analysis is based on the benefits and costs of the steeper slopes.The main benefits of the steeper working slopes lie in the delayed stripping of the waste, whereas the costs are mainly due to the failure of pit wall. The concept of probabil­ities of failure is utilized to compute the cost of failure due to steeper slopes.

The model is divided into two sub-models: 1) thebenefit-cost model, and 2) the financial risk analysis model. The benefit cost model includes all the variables that are directly affected by the changes in working slopes. It generates year by year benefits and costs associated with a given slope angle. The financial risk analysis model in turn uses these yearly benefits and costs for the full scale simulation of mining ventures and displays the results in terms of probability distributions of the decision criteria.

Two sets of computer programs were written in FORTRAN IV, one set for the benefit-cost model and the other set for the financial risk analysis model. These models were

ix

tested using a hypothetical copper ore body for their validity and applicability.

CHAPTER I

INTRODUCTION

Pit slope angle is one of the important variables to be considered in the design of any open pit mine, The mine planning engineer must decide on the ultimate pit slope angle at the outset in order to establish the geometric, limits and profitability of the mine. A steeper slope reduces the. stripping tonnage and increases the profit­ability of the mine, but, at the same time increases the probability of slope failure. A flatter slope is more stable but involves a higher stripping ratio and reduces the profitability.

Two considerations, safety and the stripping cost, govern the design of the pit slope. If safety is the main consideration, the slope angle should be kept as flat as possible so that there will be less or practically no chances of failure of the pit wall. On the other hand, if stripping cost is the main consideration, the slope should be as steep as possible to minimize waste stripping. Black (1964) mentioned these two slope angles as ’'maximum safe angle" and "minimum economic angle," respectively.

1

2

The above mentioned two extreme slopes, at least in theory, are 0° and 90°, respectively. In practice, however, the natural angle of repose of rock can be considered as the maximum safe angle. In both extreme cases the venture will not be attractive; the former due to the infinite stripping cost, and the latter due to hampered production caused by pit wall failures.

A present day problem that all mine planning engineers are facing is to determine a slope angle which is a com­promise between the two extremes. Obviously, the slope angle selected should be as steep as possible and still maintain the safe and economic conditions in the mine.

In any open pit mine, there are two different slopes that are considered by mine designers. They are: 1) theultimate slope angle, and 2) the working or interim slope angle. The ultimate pit slope is that slope which is main­tained at the boundaries of the mine and should be as steep as possible to minimize the overall stripping ratio. Any change in the ultimate pit slope angle changes the ore reserve estimates. These estimates, in turn, influence the profitability of the proposed mining venture, particularly during the feasibility study stage.

The working slope is the slope that is maintained at all other times and is mainly influenced by the working room required for the efficient operation of the mining equipment. Working slope angle in a mine with rail haulage

is flatter than in a mine with truck haulage. In a rail haulage system, the width of each bench is usually the same. In a truck haulage system, a number of benches can be combined and worked by shovel, thus increasing the overall working slope.

The economic impact of both ultimate and working slope angle is considerable, The benefit of increased ultimate slope is the decrease in overall stripping ratio. This also increases the life of the mine by increasing the ore reserve, whereas the benefit of increased working slope is in the delayed stripping which results in a higher net present value. Cost incurred in both cases is mainly due to the failure of the pit wall. The cost other than failure cost might include higher transportation cost due to steep haul road, poorer labor efficiency in working at steep slopes, etc.

Statement of the Problem , The importance of maintaining steeper pit walls in

an open-pit mine is widely accepted by the mine operators. However, presently no tool is available which can quantify the benefits and the costs resulting from the steeper slope

The thesis problem is to build a pit slope econo­mics model which will serve as the necessary investigating tool. The scope of this model, however, is limited toanalyzing the economic impact of different working slope angles.

4Review of the Related Studies

The importance of increasing pit slope angle has been mentioned by many authors. Halls (1970) discusses the economics of steeper slopes in all phases of an open-pit mine life. According to Halls, the working slope angle plays an important role in the pre-production stage and in the early years of mine life. He further states that accurate and engineered ultimate slopes are not of major importance, specially in larger deposits.

Plowman (197 0) points out that the effect of a steeper ultimate slope is to increase the amount of ore that can be mined and hence to increase the life of the mine. Increasing the life of the mine results in profits in the later years and may have little effect on the present value, of the mine.

The concept of including probability of failure and costs of failure in determination of the most economical slope angles is discussed by McMahon (1971), He gives a probability of failure curve which is the function of slope angle. He mentions that, in case of safety being the over­riding criterion, the slope angle should be that angle where the probability of failure curve becomes asymtotic to zero.In case of allowance of partial failure, he determines the cost of failure for the slide. He divides cost of failure into two parts: 1) cost of failure related to the volume, and 2) the cost of failure that is not related to the volume.

5He determines the probability of failure from the joint pattern and based on the probability he computes the expected value of cost of failure for the year.

The drawbacks of the approach adopted by McMahon are 1) he does not consider the probability of failure as a joint function of slope angle and wall height, and 2) he computes the cost of failures for all the years of the mine's life. In practice, there can be years when no failure occurs at all, and conversely, there can be many failures even in one year.

CHAPTER II

OPEN-FIT- MINE PLANNING AND ECONOMICS

The slope angle of the pit wall plays an important role in the planning and design of an open-pit mine, At the present time the determination of slope angles are based upon the rock-mechanics studies and experience of the mine operators. The common practice tends toward maintaining slopes that are flatter than necessary. This in turn defers the opportunity of substantial savings in stripping costs.

The rest of this chapter will discuss briefly the effects of pit slopes in open-pit mine planning and economics.

Ultimate Pit Slope AngleDuring the feasibility stage of the mine, accurate

determination of the ultimate pit slope angle is of minor importance. This is especially true for large deposits having a long mine life. In the earlier years of mine life, the pit wall is seldom at the ultimate slope angle. Therefore, the effect of steeper ultimate slopes is not seen until during the later years of the mine life. Benefits during the later years have practically no impact on the net present value of the property, if the mine life is over twenty years.

6

7Ultimate pit slope angle is determined after the

analysis of strength of the rock, fracture pattern, faults, and other geologic parameters. Another factor that is considered in determining ultimate slope angle is the. length of time that the slope must be stable. For a shorter time the slope can be steeper than for a longer time.

Working Slope AngleMoolick and O'Neill (1968) define working slope as

the ratio of the average bench width to the average bench height. This definition is true in most rail haulage operations and also in truck haulage operations where mining commences in a single bench pattern (Figure 1). In a single bench pattern a shovel works only one bench.

In multi-bench patterns (Figure 2) several benches are worked by one shovel. The working slope, in this case, is defined by the line joining the toes of two operating benches and the horizontal plane (AB in Figure 2).

It is clear from these two figures that the working slope is dependent upon the operating room required in an active bench, the bench height, the minimum berm width, the bank angle, and the bench pattern. Room required usually depends upon the type of equipment in use, In a rail haulage operation, operating room is needed for trolley wire, tracks, shovels, track shifting equipment and drilling and blasting equipment, In a truck haulage operation, the

Operating Bench

A x

BenchHeight

Working Slope

Figure 1. Working Slope in Single Bench Pattern

Operating Bench

BankAngle

Berm

OperatingRoom

WorkingSlope

\Figure 2. Working Slope in Multi-Bench Pattern

9room required is more for passing of trucks and for easy- spotting at the loading shovel. Moolick and O'Neill (1968) give a figure of 162 feet of working room for rail haulage and 200 feet for truck haulage operation. Soderberg and Rauch (1968) compute the required width of operating bench as 110.3 feet for a 15 yard shovel and 85 ton truck opera­tion with double spotting. For the same working room in the operating benches, the working slope can be increased by increasing the number of benches in a pattern.

The effect of steeper working slope is of great im­portance in feasibility and in earlier part of the mine life. Steeper working slope requires less amount of pre­stripping in pre-production years and lower stripping ratios in the early years of mine life. Although the stripping ratio must increase in later years of the mine life in order to catch up with postponed stripping, the net effect is to significantly increase the net present value of the mine.

Pre-Production Stripping The amount of waste that is removed to expose the

ore body before start-up of the full scale operation is called pre-production stripping. The amount of pre- production stripping depends upon the following factors:

1. Geometry of the ore body--deeper ore body re­quires larger amount of pre-production stripping. At a given depth, a flat deposit requires less amount of pre-production

10stripping to expose a given amount of ore than a tabular ore (Figure 3),

2. Working slope angle--a steeper working slope reduces the amount of pre-production stripping to expose the same amount of ore. Working slope angle should be kept as steep as possible to minimize the amount of pre-production stripping.

3. Management Policy— this is another important factor upon which the amount of pre-production stripping depends. The larger the amount of ore management decides to expose before the start of mining, the higher will be the amount of pre-production stripping. The same amount of ore as the exposed ore before the start of production is usually maintained during the life of the mine through advance stripping. In doing so, ore throughput is assured even in case of lost ore production due to unforeseen events. The amount of exposed ore depends somewhat upon the risk- taking attitude of the management personnel.

In general, pre-production stripping is done to expose enough ore for 30 day supply (Moolick and O’Neill, 1968).They have given the following generalized method to determine pre-stripping tonnage.

For 40 feet high benches with 40 feet cut, the amount of material available for each foot run will be 1600 cu. ft.,i.e., 128 tons (tonnage factor =12.5 cu, ft./ton). If management decides to have a 30 day supply, there should be

Pre-productionStripp ing

Pre-productionStripping

TabularOreBody

F la tOreBody

Figure 3. Pre-production Stripping for Two Different Types of Ore Bodies.

one foot of ore face exposed and accessible for each 4.3 tons of required daily production (128/30 = 4.3). The re­quired daily production per foot of ore face is called the factor. If the required production is 50,000 ton/day and the factor selected is 5, the ore exposed should be at least10,000 feet. In general, two to three benches are exposed instead of one. In case of two benches, each bench should be exposed for 5,000 feet. The factor that is taken as five for the above case should be taken as three in case of less flexible operation.

Mining Sequence Mining sequence in any open-pit mine depends upon

the ore grade and its geometric distribution, the management policy, equipment in use, mining capacity, haulage route, etc. A general practice is to mine high grade ores in the early years to recover money invested as quickly as possi­ble. For example, in a mine with average grade of 0.70% copper, a general practice will be to mine 1.0% copper ores in early years and 0.4% in the latter years, to maximize the net present value assuming it is possible to do so. On the other hand, management can decide to mine an average grade "of 0.7% for the entire life of the mine. However, the geom­etry of the ore body might not allow to do so.

CHAPTER III

MODEL FORMULATION

The overall structure of the pit slope economics model is outlined in Figure 4, The entire model can be divided into two major parts. Part 1 involves the modeling of an open-pit mine system to generate the results of the steeper working slopes. Part 2 concerns mostly the financial investment decision and utilizes the results obtained from Part 1 and the risk-taking attitude of the management personnel.

In formulating the model, the impact of steeper working slopes must be quantified in terms of benefits and costs. This is specially true in any kind of economic analysis. The first step is to identify the benefits and costs. It is also necessary to identify the variables that must be included in the model,

Benefits of steeper working slopes lie chiefly in the delayed stripping of the waste material. Since the ultimate slope angle is kept constant in the analysis, the overall stripping ratio does not change. The deferred stripping during early years of the mine life must be made up by additional stripping in the later years. In early years, the

■ is: .

Part

2 Pa

rt 1

V

Do Not Steepen

/ T h i s W i t / in the RiskTakini

Attitude / /

There a Chance of x. Loss ,

Yes

No Yes

/ / D o Y o u \ .Want To T a k e / Y e s sJViore Risk

No

S te ep en th e Slope

Working Slope (Base Case)

Increase the Working ________ Slope_________

Compute the Incremental Benefits and Costs.

Compute the P ro b a b il i t ie s of Decision Criter ia .

Figure 4, Schematic of the Pit Slope Economics Model.

15benefit of a steeper working slope is positive. It gradually decreases in later years until, after certain years of the mine life, it becomes negative.

The cost associated with the steeper working slopes is recognized mainly as the cost of failure of the pit wall. The problem is how to quantify the cost of failure.It is then decided to use some sort of probabilities of failure to obtain whether or not there will be a failure in a given year. In the-model, the probability of failure is input for each working slope angle as a function of wall height. The next problem is how to determine the type of failure-- if one occurs--and what the cost is to clean that up. For this it is decided that the mine operator must specify the operational impact of the failure in order that a meaningful cost can be calculated,

The variables used in modeling of the system are recognized to be of two types: 1) Those that are directlyaffected by the working slopes, and 2) those that are not directly affected by the working slopes.

To incorporate the two different types of variables in the models separately, the pit slope economics model is divided into two sub-models: 1) A benefit-cost model, and2) a financial risk analysis model. The benefit-cost model is designed to analyze the incremental benefits and costs of the steeper working slopes when they are compared to the base case. The financial risk analysis model, on the other

16is designed to perform fullscale simulation for complete financial analysis, using the results obtained from the benefit cost model.

A discussion of these two models will follow,

A Benefit Cost Model The benefit-cost model assesses the incremental

benefits and costs of steepening the working slope angle in an open pit mine. For each working slope angle, stripping costs are computed for each year of the mine life. The stripping cost for each year is compared with the stripping cost for the same year for the base case to compute the benefit. Similarly, the cost for each year (which is mainly the cost of failure) is computed for each working slope angle, and compared with the base case to obtain the incremental cost. The model also has a provision to incorporate any other benefits and costs that may occur due to steeper working slopes. The model assumes the first working slope to be the base case slope angle,

The following discussion provides an overview of the benefit-cost model.

Sectors in the PitThe pit under consideration is divided into different

radial sectors definable by existing geologic structure and rock type. It is also assumed that the geological structure within a sector is homogeneous„ The ultimate and

17working slope angles are assumed to be constant in all the sectors. This is done mainly to simplify the problem. Probabilities of failures and the operational impacts of failures whenever they occur must be defined for each sector of the pit separately.

Probabilities of FailuresThe probability of failure of the pit wall is known

to be a function of slope angle, wall height, rock type, fracture pattern, strength of rock, water table level, time, etc. Inclusion of all the variables in expressing the probability of a failure is very complex. Hence, it is assumed that rock mechanics engineers will take into account the effect of these variables in defining the probability.

In the model, the probability of a failure is estimated for each sector of the pit as a joint distribution function of slope angle and wall height (Kim, Upadhyay, and O'Neil, 1973). Since this joint distribution can be represented by two marginal distributions of slope angle and wall height, the probabilities are input as a marginal distribution of wall height only for a given slope angle.The probabilities are input as histograms having ten (10) class intervals for each slope angle and for each sector

' . i -separately.

18

Types and Frequency of FailuresTypes of failures of the pit wall considered in the

model are in terms of their operational impacts in the pit. At the present time the model has provisions for seven types of failures ranging from no cost failure to a massive failure involving plant re-locations. Operational impacts of the failures must be forecast by the mine designer for all future years of the mine life. This seems to be a very difficult task for mine operators, but it is likely that the mine operators will have a good idea of mining area and equipment locations to predict the operational impact for any future date. Operational impact has to be specified for each sector of the pit separately.

In a given sector of the pit there can be more than one failure in any one year„ This is incorporated in the model also. The sampling of the pit wall failure is done only once, but the user can specify up to three different types of failure for any sector of the pit.

Sampling of the Pit Wall FailureThe sampling of a pit wall failure from the given

probability distribution is performed by using the "Monte Carlo Method" (Kim, Williamson and Sturgal, 1973) , Samplingprocedure, in general, for a given slope angle and a wallheight is as follows:

191. Select the probability of failure curve for

the given sector and the given slope angle, Obtain the wall height for the year.

2. For this wall height, obtain the probability offailure from the probability of failure curve„ Suppose that the probability obtained is 0.4, This means that there is a 40% chance that there will be"a failure.

3. Now, generate a random between 0,00 to 1,00.If the random number is less than or equal to the obtained probability of failure, there is a failure of the pit wall. For example, if the random number is 0,6, there will be nofailure. if the random number is 0.3, there will be afailure,

There can be three distinct cases in the pit wall sampling. One is the case where the entire wall has the working slope angle (situation A in Figure 5}, The second case is situation B in Figure 5 where there are two different slopes: The upper portion is at the ultimate slope angleand the lower portion is at the working slope angle, making a kink in the slope. The third case (Figure 6) can occur when the pit wall is subjected to a "push-back,M

The sampling of the pit wall failure is straight­forward in first case because the slope angle and the wall height are uniquely determined. However, in the second case, a problem arises due to two distinct slopes and two distinct wall heights. At first, it appears that the

20

P i t Limit I n te rc ep t -Working Slope

Pre-productionStripping

U lt imateSlope

Si tuation A

\ Situation B

Figure 5, Geometry of the Pit in Different Stages of Mining.

21

PushBack

Figure 6, Geometry of the Pit in Case of Push-Back.

22average slope angle (Figure 6) and entire wall height should be used for sampling for failure. Instead, it is decided to sample the failure twice.

First, sampling of pit wall is done at the working slope angle and for the entire wall height. If no failure is observed, the second sampling is done at the ultimate slope and for the portion of the wall height that is stand­ing at the ultimate pit slope (H in Figure 7).

On the other hand, if a failure is observed in the first sampling and if it is a major failure as specified in the input data sampling of the upper portion is bypassed. A major failure is defined as a failure that involves entire wall height. Otherwise, sampling of the upper portion is conducted as stated above.

In the third case, the lowermost portion of the wall, which is subject to push-back, is considered as a separate unit and is sampled on the basis of working slope and net height (H-H in Figure 6). This wall height is used for computing cost also. The wall above the push-back is sampled separately.

In all three cases the model checks for the type of failure (if there is a failure) and branches off to the appropriate cost model to compute the failure cost.

U l t i m a t e P i t Slope

Average Slope

Working Slope

Figure 7. Geometry of the Pit Wall in Case of Kink in the Slope.

24Mining Costs

Mining costs of ore and waste material are different in different sectors of the pit. Different mining costs can be due to different rock types and the distance that the material has to be hauled. The change in mining cost due to change in the depth of the pit is specified as a trend factor.

The mining cost for the failed material can bedifferent than that of the usual mining cost. In a majority

(of cases, it is known to be higher.

Cost of FailureThe cost of failure of a pit wall can be divided into

two components: 1) the costs that are related to the volumeof the failed material, and 2) the costs that are notrelated to the volume of the failed material. The cost inthe first case will be the clean-up cost of the failedmaterial. Coates (1973) has given the following formulato compute the clean-up cost.

C = 0.08 H3 kc/vWhere C = clean-up cost ($)

k = Ratio of the unit cost for the slidematerial to the normal unit mining cost.

c = Mining cost (including drilling, blasting, loading, transportation and overhead cost) ($/ton)

v = Volume per ton of in-place failed rock (i.e., tonnage factor)

H = Wall height (in ft.)

' 25

The second type of cost which is not related to the volume of the failed material includes loss of ore, loss of production, loss of equipment,, and plant relocation,

For the details of the cost of failure model, refer to the Appendix A.

Model Assumption 1The following assumptions are made in the benefit

cost model:1. Annual ore tonnage mined is constant during ,

the life of the mine,2. Clean-up cost for minor failure is the same as

the usual unit mining cost. A minor failure is a failure that involves less than or equal to the number of benches in a bench pattern.

3. For a given sector having the same pit slope and the same wall height, the probability of failure does not change with time, •

4. Subsequent failures are independent of eachother.

5. If there is a failure in a sector in a year and if more than one failure was specified in the input data, all specified number of failures will occur in that year,

6. Types of failure, in case of a kink in slope and push-back, are identical in upper and lower portions of the slope.

267. There will be only one ’'push-back" of the pit

wall in a given sector before the first active bench reaches the ultimate pit bottom. In case of a push-back, the horizontal distance of the push-back is large enough to consider the failure of wall below the push-back independent of failure of the upper portion of the slope,

8, Working slopes are less than or equal to the ultimate slope.

Computer ProgramThe computer program for the benefit-cost model is

written in FORTRAN IV for the CDC 6400 computer and requires about 67 K words of core memory to run in FTN Compiler under the SCOPE version 3.4, The program consists of a main program and six (6) subroutines. It also has a provision to include user-supplied benefit and cost sub­routines to accommodate any other benefits and costs (other than the failure costs) resulting from steeper slopes.

There are provisions for seven (7) cost of failure subroutines out of which first three kinds are included in the program. These three kinds are thought to be applicable for all the users. They are 1) no cost failure, 2) bench failure, and 3) wall failure. The computation of cost in these failures is performed on the basis of wall height, using Coates' models (Coates, 1973).

27The output of the program is divided into yearly and

summary results. The financial summary of benefits and . costs for the life of the mine is printed for each case and for each simulation up to ten (10) simulations. The summary contains the net present value of the incremental benefits and costs for each simulation and average and standard de­viation of all the NPV's for each case.

The computer program listings are given in Appendix B and the outputs in Appendix C.

Financial Risk Analysis ModelA financial risk analysis model, developed to analyze

the economic impact of different working slope angles is not very different from the other risk analysis model in concept. However, the objective of developing this model is to use the values of incremental benefits and incremental costs generated by the benefit-cost model, and to display the fi­nancial effects of steeper working slopes.

The following discussion provides an overview of the financial risk analysis model together with a brief descrip­tion of risk analysis and Monte-Carlo sampling techniques.

Risk AnalysisIn probabilistic risk analysis, all the key variables

are estimated in terms of probability distributions. One value is selected at random from each of the distributions using the Monte Carlo sampling technique and all values

28obtained in such a manner are combined to obtain the out­come. This process is repeated many times to obtain all possible outcomes. The resulting probability distribution of outcomes are weighted in terms of their frequency of occurrences.

Monte-Carlo Sampling -■The Monte-Carlo (or simulated) sampling technique

involves replacement of universe or population by a mathematical analog. Such universe is described by an assumed probability distribution. Sampling is done from this theoretical population by means of random number table or random number generator. The procedure makes certain that each item in the population has equal chance of occurrence and that the frequency of occurrence is proportional to its probability density (Sasieni, Yaspan, and Friedman, 1959).

Decision CriteriaDecision criteria selected in this model are the net

present value (NPV), the discounted cash flow return on investment (DGFROI), and the wealth growth rate (WGR).

The net present value is defined as the difference between the present value of the positive and negative cash flows, discounted at a pre-determined interest rate (Maxim and Cook, 1972). This rate of interest should be the firm's cost of capital. The project under examination is accepted

29only if NPV is greater than zero. In case of comparison between two investments, the one with higher NPV is ac­cepted.

Two advantages of NPV are as follows:1. Net present value computation takes explicit

account of the time value of money, the economic life of the project and the cost of capital. 0

2. When used in conjunction with risk analysis, NPV not only measures risk in profitability but also measures profitability itself.

Discounted cash flow return on investment is that interest rate at which the present worth of positive cash­flows equates with the present worth of the negative cashflows (Maxim and Cook, 1972). In other words, this is theinterest rate at which NPV is zero.

DCFROI possesses all the advantages that NPV has.In addition, it does not require any "firm's cost of capi­tal." However, there are certain possible drawbacks of this method. They are:

1. In case of fluctuations in cash flows (i.e., negative, positive and again negative) this method can yield multiple values of DCFROI. Fluctuations in cash flows are not very unusual. A major pit wall failure in certain years can easily cause a negative cash flow.

2. This method implicitly assumes that the firm's re-investment rate of the positive cash flow is the same as

30DCFROI. To a great degree, this is unrealistic because DCFROI is not always equal to the possible re-investment rate.

The wealth growth rate is that interest rate at which the future value of the initial investment equates with the future, value of all positive cash flows at the firm's pre-specified re-investment rate.(Gentry, 1971).This method is more realistic than DCFROI. The re-investment rate used in computing the WGR is usually the firm's cost of capital.

The user of this model can select any one of the decision criteria for his problem. Maxim and Cook (1972) suggest net present value to be the best of all other avail­able criteria. Selection of investment criteria depends somewhat upon the company's experience. A company used to one is not likely to switch to another.

Probability DistributionThe variables used in the models are classified into

either fixed or variable type. The fixed type is slope an­gle, tax rate, depletion fate, etc., which remain fixed for the entire life of a mine as well as for entire simulations. These variables are input as a constant. The variable type will vary during the life of a mine or whose exact value is not known for certain. Examples of this type of variables are the price of copper, exploration cost, plant construc­tion cost, etc. These variables are referred to as

31stochastic variables in the model. A probability distribu­tion of all possible values for each variable is input in the model. The probability distribution can be any one of the following:

Normal Distribution. Normal distribution is perhaps the most useful continuous distribution. In a normal dis­tribution, the estimate has equal chances of occurring on both sides of some expected value with dispersion of the estimates indicated by the standard deviation. The model requires the values of mean and standard deviation.

Triangular Distribution. A distribution is assumed to be triangular when minimum, most likely, and maximum es­timates of the variable are made. The model requires the above mentioned three estimate levels for the variables and associated probabilities.

. . Rectangular Distribution. Rectangular distribution, which is also known as uniform distribution, is the one in which chances of occurrence of any event between the two extreme events, are the same. The model requires the minimum and the maximum value for the variable.

Histogram. A histogram is a graph that plots the various values of a variable and their relative frequencies. The total area of a histogram must be equal to 1. The model

32requires the minimum class limit, class interval, and the probability of occurrence for each class.

Cash Flow ComputationThe model, at present is designed to compute cash­

flows using the new Canadian tax law that will be in effect starting in 1976 (Brown, 1973a). However, this model is applicable in any other tax environment by using user's own routine(s) to compute depreciation, depletion and taxes.The method of cash flow computation is shown in Table 1.

Accelerated Capital Cost Allowance. Accelerated capital cost allowance in the new Canadian tax law is pro­vided to compensate for the loss of three year tax holiday (McDonald, 1971). Mining companies can claim 30% of the total capitalized cost or the full amount of income in a year, whichever is greater, until the full amount of depre­ciable account is recovered.

Depletion. Automatic 33-1/3 percent depletion in the old Canadian law tax has been replaced by "earned depletion" (McDonald, 1971). For every $3 of the eligible expenditure for mine exploration and development, $1 can be depleted up to 33-1/3 percent of the depletable income in that year. Due Due to the infancy of this tax law, the exact method of de­pletion calculation is not yet known. The method used in this model is as given by Brown (1973b).

33Table 1

Cash Flow Computation.

Less: Less:

Gross Income Royalty* Operating Cost

Les s:Gross ProfitAccelerated Capital Cost Allowance

Less:Income Before Exploration and Development Deductions Canadian Exploration and Development Allowance

Less:Depletable Income Depletion Allowance

Less: Less: Less:

Taxable Income Federal Income Tax Provincial Income Tax Provincial Mining Tax

Plus: Plus: Plus:

Net ProfitAccelerated Capital Cost Depletion Allowance Canadian Exploration and

AllowanceDevelopment Allowance

Cash Flow

Royalty is assumed to be some fixed percentage of gross income.

34

Taxes, Federal income tax and the provincial income tax are figured on the taxable income, whereas the pro~ vincial mining tax is figured on the income before deduction of exploration and development costs ,

Model AssumptionsLike the benefit-cost model, the financial risk

analysis model also has some assumptions, They are:1, The mine under investigation is a copper mine

with ore and marginal ore,2, Marginal ore is oxide ore which is mined and

leached on waste dump. The mining cost is zero for this ore. If the amount of oxide ore mined in any one year exceeds the capacity of the leaching plant, it goes into the inventory,

3, The work involving exploration, water and land acquisition, plant construction and pre-production stripping is to be conducted in sequential order. The total numberof years required for the above work should be equal to the specified number of pre-production years. Expenditures in each category of work are uniformly distributed to each year over the total time to complete the work.

Computer ProgramThe computer program which performs the financial

risk analysis is written in FORTRAN IV for the CDC 6400 Computer and requires about 65 K words of core memory to

35

run in FTN compiler under the SCOPE version 3.4. The program consists of a main program and fourteen (14) subroutines.

The main requirement of the program is to input yearly benefits and costs for each year and each working slope generated by-the benefit cost model. The input is from magnetic tape.

The output of the financial risk analysis is also divided into intermediate and final results. Under intermediate results, the cash flows for each year, NPV, DCFROI and WGR is printed for each working slope and for each simulation up to ten (10).

The final, results consist of the probability distributions of the increased NPV’s, DCFROI’s, and WGR’s, respectively. The probability distribution is computed on the basis of their occurrences and is divided into 23 class intervals.

The computer program listing is given in Appendix D and the outputs in Appendix E.

CHAPTER IV

MODEL TESTING

The models developed to analyze the impact of different working slope angles were tested using a hypo­thetical porphyry copper ore body, The problem was to investigate the feasibility of steepening the working slope angle from 25° to 35°. For both working slopes the ultimate slope angle was kept 45°.

The hypothetical ore body and the mine planning program used to generate the required input data for the model testing was developed at the department of Mining and Geological Engineering, The University of Arizona. An opti­mal ore reserve estimate for 45° ultimate slope angle was obtained using the mine planning program, and mining sequences were developed using 2 5° and 35° working slopes. Based on the given mining sequence, stripping ratios and ore grades were computed for each year of mine life. A pre­stripping tonnage to expose three ore benches arid three months' supply of ore at the daily mining rate of 25,000 tons of ore were also computed for both.25° and 35° working slopes. The wall heights for each sector and for each year were also determined from the mining sequences for both working slopes.

36

37

Using these mine planning data and other financial data, the benefit-cost model and the financial risk analysis model were tested in sequence. Sensitivity analyses of the clean-up cost and of the probability of failure were also conducted.

Testing of Benefit Cost ModelThe decision criterion used for this study is the net

present value of the incremental benefits and costs. A positive net present value would suggest steepening the working slope angle to 35°.

The input data used in this analysis are listed in Appendix C.

AssumptionsFor simplicity, the following assumptions were

made in the example problem.1. The pit is divided into two sectors,2. Only one type of failure is allowed in each

sector in a year.3. Throughout the life of the mine, only the first

three types of failures are allowed. Furthermore, these failures are assumed to occur in sequence of type 1, type 2 type 3; type 1, type, type 3, . . . , starting from the first year of prestripping. Failure type 1, type 2 and type 3 represents no cost failure, failure involving the benches equal to the number of benches in the bench pattern and

38failure involving entire wall height respectively.

4. The clean-up cost for the second type (bench failure) of failure is the same as the regular unit mining cost.

5. In case of a large failure, the clean-up cost is higher than the regular unit mining cost. A large failures is considered to be the one that involves entire wall height. The clean-up cost is taken as 1,25 times the regular unit mining cost if the clean-up is done by the company and 3.0 times if outside contractors are used.

Discussion of the ResultsThe intermediate results (Table 2 through Table 5)

include yearly benefits and yearly costs for both working slope angles. For each simulation, the incremental benefits of 35° compared to that of 25° working slopes are 0 in the first five years, because of having no mining activity. In the pre-production years (years 6 through 8) the benefits are about 2 1/2 million dollars for each year. Again, from years 9. through 18, the benefits are positive but decreasing. The reasons for this is the decreasing stripping ratios. From the year 19 to the end of mine life, with exception of years 23 through 28, the benefits are negative and decreasing. The years 23 through 28 have no benefits because of stripping ratios being the same for both cases.

The costs, which are based on sampled failures, are quite randomly distributed. The incremental costs for 35°

39Table 2

Annual Incremental Benefits for Working SlopeAngle of 25°.

lAK STK.CUb1 [jfc.i'iC.F 11 OTHctt BENEFITI v, 0. 0.z U, 0. o.3 0, 0, o.4 0, 0. 0.b u. 0. 0.b bbHJObb, 0. 0.V d Z1Jdbu• 0. 0.6 OddbGOb, 0. o.y 14430742, 0. 0.lv i'+71V3b7, 0. 0.il lb16093/. 0. 0.xa 7949330, 0. 0.i.) dlbfdlu. 0. 0.14 6433444, 0. 0.lb ti06u44 Z, 0. 0.16 6947040. u. 0.17 92lb4bl, 0. 0,lu 949191b, 0. 0.19 HbC33l4. 0. 0.Lb 092 3214. 0. 0.cl 9260142, 0. 0.9cbI34b, 0. 0.o49004Z, 0. 0.a 4 o749o4o . 0. 0.Cu Zu19634. 0, 0.Co 7300420. 0. 0,cz 7392436. 0. 9,Cb 769o 134, 0. 0.Z'J 27u332c. 0, 0,oO 261 l4bb. 0. 0.31 2923913. 0. 0.32 3040670, 0. 0.36 JiocbOb. 0. 0.

TOTAL BENEFIT

oo

oo

co

oo

oo

co

oo

oo

oo

oo

oo

oo

oo

oo

oo

oo

40Table 3

Annual Incremental Benefits for Working SlopeAngle of 35°.

'I t An 0 1 H.COOT b u ^ L F i l 0TH6R bENLf- .IT TOTAL be me

X (•. 0 . 0 , 0 .a u , 0 . 0 , 0 .j u , 0 . 0 , 0 .'4 (2 . 0 . 0 . 0 .

u , n . 0 , 0 .o o j 5 3 2 3 1 , 2 3 8 1 0 3 3 . 0 , 2 3 6 1 8 3 3 .7 Ucti . toVo, 2 4 2 9 4 7 U. 0 , 2 4 2 9 4 / 0 ,3 o4U7U2' , . 2 4 7 8 0 3 9 . 0 , 2 4 7 3 0 5 9 ,V U L l b l V b . 3 2 1 5 5 4 6 . 0 , 3 2 1 5 5 4 6 ,

l u 1 1 4 0 v 5UU, 3 2 7 9 b 3 6 . 0 , 3 2 7 9 8 5 6 .11 1.1 7ddot iu . 3 3 7 6 2 5 2 . 0 . 3 3 7 8 2 5 2 .It- oC 4 9 0 VOj 149934 0 . 0 , 1 4 9 9 3 4 0 ,10 uo:40'f VO , 1 5 4 4 2 2 0 . 0 , 1 5 4 4 3 2 0 .14 Ub4a79H. 1 3 9 0 6 4 9 , 0 , 1 3 9 0 6 4 9 .15 7u4 o 07 t i , 1 C 3 63 69 , 0 , 1 8 3 6 3 6 9 ,I d 7 2 5 9 5 2 0 . 1 8 8 7 3 2 0 , 0 , 1 6 8 7 5 2 0 ,17 7 4 7 730 o. 1 7 3 5 1 4 b . 0 . 1 7 5 6 1 4 6 .i o 77 u i o 2 o . 1 7 9 0 2 9 0 . 0 , 1 7 9 0 2 9 0 ,I V 1u 5 7 b d 9 o , - 1 9 1 3 3 0 3 . o . - 1 9 1 3 5 6 3 .

1 0 6 9 4 2 0 4 . - 1 9 7 0 9 9 1 , 0 . - 1 9 7 0 9 9 1 .c l 1 1 3 2 9 9 7 2 . - 2 0 4 9 3 3 0 , 0 , - 2 0 4 9 0 3 0 ,

1 1 7 8 3 1 7 1 . - 2 1 3 1 6 2 4 . 0 . - 2 1 3 1 0 2 4 .ao 6 4 9 0 0 4 7 , 0 . 0 , 0 ,a 4 o74 9 6 4 o , 0 , 0 , 0 .au 7 o l 5 6 3 4 # 0 . 0 , 0 .ab 7 3 0 0 4 ^ 0 , 0 . 0 , 0 .a 7 75 9 2 4 3 b , 0 . 0 . 0 ,a t 7.89c. 134 , 0 . 0 . 0 .

7293c 70 , - 4 5 9 0 5 4 7 . 0 , - 4 5 9 0 5 4 7 .JO 7 5 b 5 6 2 4 . - 4 7 7 4 1 6 9 . 0 , - 4 7 7 4 1 6 9 .31 7 6 6 9 0 4 9 , - 4 9 6 5 1 3 6 , > 0 . —4 9 6 5 1 3 6 ,Od 02.0461 j , - 5 j . o 2 7 4 l , 0 , - 5 1 6 3 7 4 1 ,oo 0 3 3 2 7 9 b . - •3 37 02 91 . 0 , - 5 5 7 u2 9 1 .

Table 441

Annual Incremental Costs of Working SlopeAngle of 25°.

YlaK FAJLL.CvuT UUiEK COST TOTAL COST

o'♦Su7o0lu111cId1lbio17lcIVZUcl2ccd242bcuc 7262V60dldcdd

u.u,V.o,U.L.120,0,0,0.

‘fSZuOdl. U,o.u ,0.ISb,0.u.

17o.0.U.

16V, 2ol62bV.U.

l> #2569591. u,

476. 104V266.

0. 26V. 27ti4b9bd.

0.

0.U.0.0.0,0.0,0,0.0.0.0.0.0.0.0.0.0.0.0.0.0.0,0.0.0.0.0.0.0,0.0.0.

n00000

12d000

4S200dl0000

15500

1700c

1692616259

00

25595910476

10492080

26927645953

0

INC. COST0. 0. 0. 0. 0. 0. o-, 0.o

o o

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42Table 5

Annual Incremental Costs for Working SlopeAngle of 35°.

rAlL.CObi OlrlEK C051 TOTAL COST INC. COSTi U, 0. 0 , 0 .c. u. 0 . 0 , 0 .w» 0 . 0 . u. 0 .4 u. 0 . 0 , 0 *b 0. 0 , . 0 , 0 .b V • 0 . u. 0 .7 0 . 0 . 0, -123.o 0 . 0 . 0, 0 .9 0 . 0 . 0. 0 .10 0. 0. 0 , 0 ,11 u. 0. 0 , -4520031.

0. 0. 0 , 0.lb v * 0. 0, 0 .14 5449722, 0 . 5449722, 5449722.1:> o. 0 , 0, 0.lb c. 0. 0. -165.17 u. 0 . 0 , 0 .lb u. 0. 0 , 0 .19 u. 0 . 0, -170.2U i59256, 0 . 159236. 159236.ki 0 . 0 . 0. 0.0. 0. 0. — 109«

559812. 0. 539012. -2076446.24 0 . 0 . 0, 0 .25 425. 0. 425. 425.2b Ib999670, 0. 13999670, 11440079,27 o . 0 . 0 . 0 ,2b 47o. 0. 478, 0 ,29 15747725, 0 . 15747 725. 14696457,bo 0. 0. 0 , 0 .wl 536. 0. 530, 269,52 223816/0 , 0. 22301676, -5464277,bb 0. 0. 0. 0.

43slope in some years are negative. This is because there were failures for 25° working slope and none for 35° working slope in those years. The third type of failure (which is assumed to occur every third year), has given an increasing trend to the cost of failure, with one exception involving the push-backs.

The final results of four different runs are tabu- labed in Tables 6, 7, 8, and 9. Tables 6 and 7 contain the results of sensitivity analysis on the clean-up Cost and Tables 8 and 9 contain the sensitivity analysis on the probability of failures. The net present values of the incremental benefits and costs are computed at a discount rate of 15%.

Table 6 shows that the increase in clean-up cost from 1.25 times to 3.0 times the unit mining cost reduced the net present value from 4.72 million dollars to 3.14 mil­lion dollars, and increased the chances of negative net present value from 0% to 10%. Similarly, for 25% higher probability of failure, the increase in clean-up cost from 1.25 times to 3.0 times the unit mining cost reduced the net present value from 4.42 million dollars to 2.41 million dollars, and increased the chances of negative NPV from 0% to 20% (Table 7)*

Keeping the clean-up cost constant to 1.25 times the unit mining cost, the increase in probability of failure by 25% reduced the NPV from 4.72 million to 4.42 million

Table .6

Sensitivity Analysis of Clean-up Cost on the Incremental Net Present Values of 35° Slope Over 25° Slope (At Standard Probability of Failure Values*).

Mining Cost Used

Inc. NPV Million $

Standard Deviation (Million $)

Negative Inc. NPV out of 100 Simulations

% Chance that Inc. NPV will go Negative

1.25 times the unit mining cost

4.72 1.04 0 0

3.00 times the unit mining cost

3.14 2.51 10 10

Standard values refers to the probability of failure curves that are used for the analysis.

Table 7

Sensitivity Analysis of Clean-up Cost on the Incremental Net Present Values of 35° Slope Over 25° Slope (At 25% Increased Probability of Failure*).

Mining Cost Used

Inc. NPV Million $

Standard Deviation (Million $)

Negative Inc. NPV out of 100 Simulations

% Chance that Inc. NPV will go Negative

1.25 times the unit mining cost

4.42 1.07 0 0

3.00 times the unit mining cost

2.41 2. 5.7 20 20

For each slope angle the probability of failure for each wall height has been increased by 25% to test the sensitivity (cumulative probability is less than or equal to 1.00).

Table 8

Sensitivity Analysis of Probability of Failure on the Incremental Net Present Values of 35° Slope Qver 25° Slope (Clean-up Cost at 1.25 times

the Unit Mining Cost).

Probability of Failure

Inc. NPV Million $

Standard Deviation (Million $)

Negative Inc.NPV out of 100 % Chance that Inc. NPV Simulations will go Negative

Standard Value* 4.72 1.04 0 025% Increase in 4.42 1.07 0 0Probability ofFailure**

^Standard value refers to a probability of failure curves that are used for this analysis.

**For each slope angle, the probability of failure for each wall height has been increased by 25% to test the sensitivity (cumulative probability is less than1.00).

Table 9

Sensitivity Analysis of Probability of Failure on the Incremental Net Present Values of 35° Slope Over 25° Slope

(Clean-up Cost at 3.00 Times the Unit Mining Cost).

Probability of Failure

Inc. NPV Million $

Standard Deviation (Million $)

Negative Inc. NPV out of 100 Simulations

% Chance that Inc. NPV will go Negative

Standard Value* 3.14 2.51 10 1025% Increase in Probability of Failure**

2.41 2.57 20 20

^Standard value refers to a probability of failure curves that are used for this analysis.

**For each slope angle, the probability of failure for each wall height had been increased by 25% to test the sensitivity (cumulative probability is less than1.00).

48dollars. The chances of negative net present value, how­ever, remained the same (Table 8). For the clean-up cost of 3.0 times the unit mining cost, the increase of probability of failure by 25% reduced the NPV from 3.14 to 2.41 million dollars and at the same time increased the chances of nega­tive NPV from 10 to 20% (Table 9).

The results discussed above leads to the conclusion that the increase in probability of failure has less impact on the lower clean-up cost and has higher impact for higher clean-up cost, assuming all other conditions and data are valid.

Testing of Financial Risk Analysis Model Yearly benefits and costs for each working slope

that are written on the magnetic tape by the benefit cost model are read in as part of theinput data to the financial risk analysis model. The working slopes to be tested are 25° to 35°. All other data used are included in Appendix E.

Four different runs are made for the same four cases discussed in the benefit cost model testing.

Discussion of the ResultsThe intermediate results (Table 10) consists of the

cash flows for each year, NPV, DCFROI and wealth growth rate for each working slopes. It also consists of the sorted values of the increased NPV, DCFROI and WGR for 35° working slope compared to the 25° working slope (Table 11).

Table 10

Intermediate Results Showing Annual Cash Flows and Associated NPV, DCFROI, WGR for Each Slope Angle

Discount Factor Used = 15%.

' WORKING SLOPE ANGLE = 25'CASH FLOWS FOR YEARS 1 THROUGH 33■Ivc6v7• —16G6b7•

22tiScCul. 232fca3t>3. liie.;.2£>}7 * 17V829&8. 1<;7411>4. -5273196. ,/rV = 2031U3G7. uCFROI = 21.630 »GR = .171

—166667. 20663133. 13443081. 19366302.

-500000.20012463.19105925.

-500000.19523193.18265013.

-21206731.19121867.18516433.

-21377532.9529046.13354924.

-21551749.13493241.18064450.

29711477.18616236.9684750.

2607o:C"'. 1742C14 t. 19915993.

*OFKl.NG SLOPE ANGLE = 35-CASH FLOWS FOR YEARS 1 THROUGH 33

—lbG6u7• —166607. 24129918. 22*61776. 17145565. lodl1259. 17o-.25E6. -235*3646. t.PV = <3281371. uCFROI = 24.200 tiGR = .175

-166667. 20734070.3395400.17049247.

-500000.20379715.19096653.

-500000.20074455.18658939.

-18324397.19809541.17568222.

-18948062.19574070.13352195.

-20974434.19356705.18082622.

32183060.. 17717704. 1174829.

250.96081. 1746^791. 17921271-.

10

50Table 11

Sorted Values of Increased NPV, DCFROI and WGR for 35° Working Slope Compared to 25°.

S I M U L A i I O h liPv WGR

i - l b d 8 M G 9 . . 4 0 0 .cooc - 5 7 2 1 0 2 . l.ioo .001

- 3 2 4 1 0 b , 1 . 2 0 0 .0014 - 1 6 5 4 1 7 , 1 . 5 0 0 . 0 0 2b 1 5 2 1 4 2 . l .b O O . 0 0 2b 4 ‘t 9 o 6 b , 1 . 6 0 0 , 0 0 ?1 6 7 1 7 3 5 , 1 . 7 0 0 . 0 0 2

6 9 6 1 6 9 , 1 . 5 0 0 . 0 0 39 1 0 0 4 6 0 2 , 1 . 9 0 0 . 0 0 3

10 1 1 6 9 0 9 4 , 1 . 9 0 0 . 0 0 311 1 2 5 4 2 6 9 , 1 . 9 0 0 . 0 0 31L 1 3 2 9 3 2 0 , 2 . 0 0 0 . 0 0 3Id 1 5 4 6 1 0 3 , 2 . 0 0 0 . 0 0 3I s 1 5 4 9 1 4 5 , 2 . 1 0 0 . 0 0 3l b 1 7 2 0 6 5 4 , 2 . 5 0 0 . 0 0 3l b x0 0 3 2 6 6 , 2 . 5 0 0 . 0 0 317 1 9 0 6 2 2 9 , 2 . 5 0 0 . 0 0 316 1 9 5 0 4 5 5 , 2 , 5 0 0 . 0 0 319 1 9 7 0 5 2 5 . 2 . 4 0 0 . 0 0 3Zb 2 0 IMS3 0 , 2 . 4 0 0 . 0 0 321 2 0 5 9 6 9 2 , - 2 .M 0 0 . 0 0 322 2 0 5 5 4 0 5 , 2 . 4 0 0 . 0 0 42 b 2 1 1 2 7 6 7 . 2 . 4 0 0 . 0 0 424 2 1 2 0 2 6 7 , 2 . 4 0 0 . 0 0 42b • 2 1 3 6 6 7 2 . 2» 50 0 . 0 0 42 ci 2 1 6 7 2 1 6 , 2 • b00 . 0 0 427 ‘ 2 2 6 3 5 6 7 . 2 . 6 0 0 . 0 0 42o 2 3 0 6 1 9 1 . 2 . 6 0 0 . 0 0 429 2 3 0 9 7 0 1 , 2 . 6 0 0 . 0 0 4JO 2 3 2 9 9 4 9 , 2 . 6 0 0 . 0 0 4J l 2 3 k 6 2 7 / . 2 . o 0 0 .004J2 2 3 5 2 0 5 5 . 2 . 6 0 0 . 0 0 4bb 2 4 0 5 7 9 5 . 2 . 6 0 0 ' . 0 0 4b4 2 4 6 7 2 3 0 . 2 . 6 0 0 . 0 0 4bu 2 8 ’J 4 22 , 2 . 6 0 0 . 0 0 4bo 2 0 5 3 7 9 6 , 2 . 6 0 0 . 0 0 437 2 9 4 1 6 9 3 . 2 . 6 0 0 . 0 0 43b 29fcb43u , 2 . 6 0 0 . 0 0 439 2 9 7 0 9 7 5 , 2 . 7 0 0 . 0 0 44u 5 0 4 0 5 1 2 . 2 . 7 0 J , 0 0 441 5 0 9 1 4 3 4 . 2 . 7 0 0 . 0 0 442 v l 70 060, 2 . 7 0 0 . 0 0 4Mb 3 2 3 6 711 . 2 . 6 0 0 . 0 0 4M4 5 2 s 1 5 0 1 . 2 . 6 0 0 ,00bMb 5354 5 5 b . 2 . 9 0 0 . 0 0 5MO 5 3 9 5 4 7 1 . 2 . 9 0 0 .0054 7 - 5 6 9 4 9 3 . 2 . 5 0 0 . 0 0 5MM 5 t o 0 i 7 b , 3,000 . 0 0 549 4 0 16b7t-' . 3 . 1 0 0 , U 0 5bU 4 9 0 9 5 4 5 . 3 . 2 0 0 . 0 0 6

51Using a clean-up cost at 1.25 times the unit mining

cost, the incremental net present values obtained from the benefit-cost model for both cases are positive for all simu­lations. (See Tables 6 and 7.) However, the result ob­tained from the financial risk analysis model, using the results of the benefit cost model, shows four negative values of the incremental NPV. This shows that the complete financial analysis does change the picture of the outcome.

The final results for the four different risk analy­sis runs are tabulated in Table 12 to compare with the re­sults obtained by the benefit cost model. Only the net present values are used for the comparison purpose. For other criteria, refer to Appendix E.

Comparison of the results obtained by the financial risk analysis model to the one obtained by the benefit cost model shows that, with clean-up cost at 1.2 5 times the unit mining costs, the chances of negative NPV’s are 8% and 2% from the financial risk analysis, whereas 0% and 0% from the benefit cost analysis. Similarly, in case of the clean-up cost at 3.0 times the unit mining cost, the chances of nega­tive NPV s are 62% and 72% as compared to 10% and 20%.

For the identical clean-up cost, the increase in probability of failure by 25% does not change the probabil­ities of NPV’s going negative by big amounts.

The comparison of outputs of the two different models show that the complete financial analysis is

Table 12

The Results Obtained by the Four Different Runs of the Financial Risk Analysis Model. -- Sensitivity analysis on prob­

ability of failure and clean-up cost.

'^Probability of ^\Failure

Standard Value of Probability of.Failure*

25% Increased in the Probability of Failure**

Clean-up^\. Cost

Probability of Achieving at Least Zero Inc. NPV

Probability of Achieving at Least Zero Inc. NPV

1.25 times the unit mining cost

92% - 98%

3.0 times the 38% 28%unit mining cost

*Standard value refers.to the probability of failure curves that are used for the analysis.

**For each slope angle the probability of failure for each wall height has been increased by 25% to test the sensitivity (cumulative probability is less than or equal to 1.00).

53desirable for analyzing the impact of working slope angle in the open pit mining feasibility study.

CHAPTER V

CONCLUSION AND RECOMMENDATIONS

ConclusionsThis thesis has given guidelines and has presented

a feasible way of analyzing the impact of different working slope angles on the overall open pit mining economics, by utilizing the concepts of probability of failure and the cost of failure, However, the problem is very complex due to interaction of many variables, A detailed study of mine planning is essential prior to the pit slope economics analysis.

The results obtained from the model testing are entirely based upon the hypothetical data and hence the results that can be obtained in the real life situation may be different, However, benefits of delayed stripping due to a steeper working slope occur in the early years whereas costs of additional stripping are mostly in later years. Thus, the net present value of a steeper working slope is positive. It cannot be said that continuous increase of the working slope angle from one to another will always increase the net present value. There will be a point beyond which any increase in the working slope

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will decrease the net present value due to many failures of the pit wall,

RecommendationsIn order to make the benefit cost model more

practical and suitable to different conditions that are existing in open pit mines, the following improvements and further studies are recommended.

1. The assumption of maintaining the same working and ultimate slopes in all sectors in the pit should be eliminated, since difference in the strengths of rock can justify steeper slopes than another. Hence the model should be designed to handle different ultimate and wofking slopes in different sectors of the pit.

2. The model should be revised to analyze the impact of different ultimate slopes also,

3. The model which is designed for a massive deposit such as the porphyry copper deposit should be made more general to be applicable for other type of ore body.

4. The model in which a pit is assumed to have near vertical (or radial) sectors only should be modified tohave relatively horizontal sectors also. This is particularly desirable for a tabular deposit where the geology changes considerably with the height of the wall,

5. Cost models are one of the important factorsto be considered in any pit slope economics study and hence there is a need for development of other cost models.

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6. The probability of failure which is another important variable to be considered for this study should not be overlooked. The probability of failure which is considered to be the function of slope angle and wall heights should be tested for the validity of the approach.

7. Sampling proceedure should be improved to reduce some of the simplifying assumptions.

8. The amount of input data required in the benefit cost model is large. Hence the model requires an improve­ment of the input data handling procedure.

APPENDIX A NOTES ON COST OF FAILURE

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58These notes on cost of failure include a brief de­

scription of the cost models given by Dr. Coates (Coates, 1973) and the cost models incorporated inthe benefit cost model.

Dr. Coates' Cost ModelsDr. Coates divides the total cost of failure of a

pit wall into the following three components:1. Cleanup/unloading/postponed production - There

can be three cases in this component of cost. In the first case the failure of a pit wall is assumed to have occurred. The slide material is cleaned up to resume mining. The second case, where the slide has not yet occurred, but the ground is moving, might require unloading of the unstable material. The third case is to postpone the production in the area where unstability has occurred or predicted. The computation of cost in all the cases is based upon the height of the pit wall.

Clean up Cost. The clean up cost

Cc = 0.08 H3 kc/V

Where Cc = Clean up cost ($)H = Height of the wall (ft.)k = Ratio of the unit cost for the slide

material to the normal unit mining costc = Mining cost (including drilling, blast­

ing, loading, transportation and overhead cost) ($/ton)

v = Volume per ton of in-place failed rock, (i.e., tonnage factor)

In deriving the formula, it is assumed that a fail­ure of the pit wall involves back-break at the creast 0.2 times the height of wall and width of the slide (parallel to the face) is 0.5 times the height of the wall.

Unloading - The cost of unloading

Cu = 0.08 H3 kc/v

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Variables used to derive cost of unloading (Cu) is same as in clean up cost.

The assumptions made to obtain above relationship are;1. Width of stripping at crest equal to 0.4 times

the height of the wall (H),2. Breadth of stripping parallel to face equal

to the height of the wall.5. Depth of stripping equal to 0,2 times the

wall height.Postponed production - The cost of posponed

production,Cp = 0,07 H3 p/vWhere Cp = Cost of postponed production ($)

H = Height of the wall (ft)p = Profit ($)/ton of ore and depends upon

grade of orev = Volume of failed material in place

(cu. ft.)2. Increased transportation cost,- In case of the

failure of a ramp system, a new ramp has to be re-established to resume mining. There can be two components of costs.First to construct a ramp system and second, the cost due to increased haul distance.

The general formula for the volume of excavationneed is

V = WD2/2GWhere W = Width of the ramp (ft)

D = The depth to the previous ramp elevation at the mid-point of the design sector (ft)

G = Grade of the ramp

60The cost of excavation:Cg = VxCWhere C = Unit cost of excavation ($/cu.ft,)The cost due to increased haul distance can be

computed as follows:

C i n > QL C t

Where C• = Extra cost due to increased hauldistance ($)

Q = Annual quantity hauled over the extra distance (ton)

L = Extra distance (ft)Ct= Unit cost of transportation ($/ton mi)

The total cost due to the failure of the ramp systemcT = cE + cin3. Plant relocation - When instability of the pit

wallwarrants the relocation of the nearby plant (e.g., crusher, water tank or complete mill), the cost of relo­cation of such plants are considered as the cost of failure.

Cost of Failure Types Incorporated in the Model

There are currently three types of failure in the benefit-cost model. Cost models for each type of failure has to be supplied as subroutines. Subroutines for first three types of failures are thought to be applicable to nearly all users and is provided in the program. However, the user of the program can include all the cost models that are suitable for their condition.

1. No cost failures - This failure refers to the type that involves no extra cost. In some cases, small failure can become an advantage rather than disadvantage.

2. Bench Failure - These are minor failures which might involve one or more benches depending upon the bench pattern in use. In a single bench pattern, only one bench is assumed to fail. In multiple bench pattern, the composite height of all the benches within this pattern is assumed to fail.

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3. Wall Failure - This type of failure involves the entire wall height. Cost of failure can be calculated using a cost model such as the one given by Coates.

APPENDIX B THE BENEFIT COST MODEL COMPUTER PROGRAM

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PROGRAM HEMCST ( I f l PUT »Q' JTPl j r « T APE1 = I N 3 UT , T A P F ? = O U T P U T , P U N C H , T A P F 4 )

T H I S PROGPAM READS I N RUN P A P A M E T E R ( O P T I O N ) C A RD, CA L L S S UBROUT I NE S TO READ DATA AN) TO CALCULATE I NCREMENT AL 1 E N E F I T S Awn COS T S . CALCULATED I NCREMENTAL B E N E F I T S AND C O S T S , DEPENDI NG UPON THE NEED OF THE U S E R , E I T H E R PUNCHED ON CAROS, WRI TT EN ON TO THE MAGNETI C TAPE OR P R I N T E D .

RAJA P. UPADHYAY DE P T . OF M I N . AND GEOL. ENG. U. OF A.

D I M E N S I O N S T t) ( 3 >C O M M O N 1 O P T H , T O P T C , N U L S L , N S E C , N S L O P , N ° P O C , N H N P A T ,N Y P R , N N ,R E N H T ,N T , 1 C A P A C , N W R S L (3) , P T 0 N ( 3 ) , C O S T M (3,5) , STRIP?. ( 3 , 32 ) , R A T I O (5) , V O L ( 5 ) , S T E ? L C V (5) , B 0 T P T T ( 3 , 5 , 6 3 ) , R O T U L T ( 3 , 5 , 6 3 ) , P P 0 3 ( 3 , 5 , m , H E I T ( tC) , I T Y P E ( 5 3 , 6 0 , 3 ) , M A X , N Y ( 5 ) , P E R ( 5 ) , N B U G , L H T , N P R I N T . N A M E (20) , N S I M , R R A T EC O M M O N / R A J / A R S T P ( 3 ) , E E N S T (3, 60) , R E N O T ( 3 , 6 0 ) ,D E N I N C 3 , 6 0 ) ,X C O S K 3 , 6 0

1)C O M M O N / t M A / F C O S T ( 3 , 5 , 6 0 ) , O T C O S T ( 3 , 5 , 6 0 ) , T C O S T ( 3 , 5 , 6 0 ) , C O S T N ( 3 , 5 , 6 D 1 ) , C O S T I N ( 3,601 , F F C S T ( 3 , 6 0 ) , T O C S T ( 3 , 6 0 ) , T C T ( 3 , 6 C )C G M M O N / R P U / C U P R O O ( 3 , 5 , 1 C ) , P F A I L < 3 , 5 , 6 0 ) , N F A I L ( 3 , 5 , 6 G ) , U L T H T ( 3 , 5 , 6 0 1)C O M M O N / L I F E / N O , A N R V U ! , PV( 10 0, 3)C O M M O N / T R E N Z C O M N ( 3 , 5 , 6 0 ) ,A C O S T (60)I O P T B = O P T I O N F O R U S E R S U P P L I E D S U B R O U T I N E D E N E F 2 , 0 M E A N S NO,1 M E A N S YES. IF YES , T H I S P R O G R A M W I L L C A L L 9 E N E F 2 I O P T C = O P T I O N F O R U S E R S U P P L I E D S U B R O U T I N E C 0 S T 2 , 0 M E A N S NO,1 M E A N S Y E S , I F YES , T H I S P R O G R A M W I L L C A L L C O S T 2 N B U G = P R I N T O U T O P T I O N F O R D E B U G G I N G , 0 M E A N S NO, 1 M E A N S Y E S N O U T = I N P U T D A T A P R I N T O U T O P T I O N , 0 M E A N S NO, N C N Z E R O M E A N S YES N P R I N T = O U T P U T O P T I O N , = 1 P U N C H IN C A R D S A N D P R I N T

= 2 W R I T E IN M A G N E T I C T A P E AND P R I N T = 3 P R I N T O N L YR E A D I D E N T I F I C A T I O N C A R DR E A D 9 , N A M E 9 F O R M A T (2 j A A )R E A D T H E O P T I O N C A R DR E A D 1 0 , I O P T D , I O P T C , N 3 U G , N O U T , N P R I N T 10 F O R M A T (5110)C A L L S U B R O U T I N E RE A D I N TO R E A D T H E I N P U T D A T A C A L L RE A O I N

C H E C K IF I N P U T D A T A IS TO RE P R I N T E D I F (N O U T .L T ,1) G O TO 20C A L L S U D R O U T I N O U T P U T TO P R I N T I N P U T D A T AC A L L O U T P U T

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20 P R I N T 3030 F0 P;iA T (1H 1 « 35X ♦ * RESULTS *///!

P R I N T 1 1 , N A M E 11 F O R M A T (lCX,23At4//>P R I N T 1515 FORMAT (ACX,* IN TERMEDIATE RESULTS*///#

S I M U L A T E AS M A N Y T I M E S AS R E Q U I R E ] .00 AO IS = 1, N S I MC A L L S U B R O U T I N E B E N E F I TO C O M P U T E I N C R E M E N T A L B E N E F I T F O R E A C H W O R K I N G S L O P E S W I T H R E S P E C T TO THE R A S E C A S EC A L L G E N E FIC A L L S U B R O U T I N E C O S T 1 T O C O M P U T E I N C R E M E N T A L C O S T F O R E A C H W O R K I N G S L O P E S W I T H R E S P E C T TO T H E B A S E C A S EC A L L C O S T 1O U T P U T SG O T O (110, 1 2 0 , 1 3 0 1 f N P R I M T P U N C H T H E R E S U L T S IN C A R D S

110 D O 111 I = 1,N S L C P D O 111 KK = 1 , NOP U N C H 1 1 2 , K K , X C O S T ( I , K K ) , B E N S T (I , K K ) , B E N O T (I , K K ) ,B E N I N (I ,KK)112 F O R M A T ( 1 1 0 , 4 F 1 5 . 0 )111 C O N T I N U EDO 113 I = l . N S L O P

D O 113 K K = 1 , NDP U N C H 1 1 2 , K K , F F C S T (I , K K I , T O C S T (I , K K I , T C T (I , K K 1 , C O S T I N ( I , KK)1 1 3 C O N T I N U E P R I N T 140

140 F O R M A T C / 1 0 X , * A L L O U T P U T P U N C H E D IN C A R D S * / / )G O TO 130W R I T E T H E R E S U L T S IN T H E M A G N E T I C T A P E

120 DO 121 I = 1 , N S L O P D O 121 KK = 1 , NOW R I T E (4, 122) ACOST.(KK) , X C O S T (I , KK).,BENOT (I , K K ) , TCT ( I , K K )122 F O R M A T ( F 5 . 3 , 3 F 1 0 . 0 )121 C O N T I N U E P R I N T 15 G150 F O R M A T < / l O X , * A L L O U T P U T W R I T T E N I N T O T H E M A G N E T I C T A P E * / / )

P R I N T T H E B E N E F I T S130 I F ( N B U G . E O . 0) GO TO 300 I F ( I S . G T . 10) G O TO 300

P R I N T 5, IS5 F O R M A T ( / 1 3 X , * S I M U L A T I O N N U M B E R * , I 4 , / / 2 X ,*1 . B E N E F I T - * / )DO 72 I = l , N S L O r>P R I N T 7 5 , N W P S L ( I )

75 F O R M A T ( / / 2 0 X ,*W O R K I N G S L O P E A N G L E = * , I 2 / / 5 X , * Y E A R * , 1 0 X , * S T R . C O S T * 1 , 5 X , ' B E N E F I T * . 5 X , * O T H F R B E N E F I T * , 5 X , ' T O T A L B E N E F I T * / )

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n o 7 0 K K = 1 « M 0P R I N T ?>?, KK, Y C O S T ( I, KK) , B E N S T ( I,K K> , BE N O T ( I, KK> , B E N IN 1 1 , K K ) f>? F O R M A T ( 1 8 , 4 X , U F 1 5 . 0 )70 C O N T I N U E

P R I N T C O S T SP R I N T ^

6 F O R M A T ( / / 2 X , *2. C O S T - * / ) no 1C 1 1 = 1 . N S L O ?P P I N T 10 2 » N W ^ S L ( 1 110? F O R M A T ( / ? C X . * W O R K I N G S L O P E A N G L E = * , I 3 / / 5 X . * Y F A P * . 1 O X , * F A I L .C O S T *

1 5 X , * O T H E R C O S T * , 5 X . * T O T A L C O S T * , S X » * I N C . COST*/)00 101 KK = 1 . NOP R I N T 10 3 , K K . F F C S T ( I , K K ) , T O C S T ( I , K K ) ,T C T C I , K K ) tc n S T I N C I , K K )

1 0 3 F O R M A T ( T 8 . A X . A F 1 5 . 0)101 C O N T I N U EC A L L S U B R O U T I N E N E T P V TO C O M P U T E T H E N E T P R E S E N T V A L U E OF T H E I N C R E M E N T A L B E N E F I T S A N D I N C R E M E N T A L C O S T S .

300 C A L L N F T P V ( I S )40 C O N T I N U EP R I N T T H E NPV F O R E A C H S I M U L A T I O N .P R I N T 660

6 6 0 F O R M A T ( 1 H 1 , 4 0 X . * F I N A L R E S U L T S * / / / )00 701 I = 2 , N S L O 0 P R I N T 6 0 1 » N W R S L ( I )601 F O R M A T { 1 C X . * W O R K I N G S L O P E A N G L E = * . I 3 / / 5 X , * S I " U L A T I O N * ,1 1 u X «* NPV OF INC. R E N . A N D INC . C O S T S * / )

DO 701 IS = 1 , N S I M P R I N T 6 G C . I S . ° V ( I S . I )650 F O R M A T ( I 1 1 . F 3 0 . 0 )7 0 1 C O N T I N U EP R I N T 5 0 0 , N S I M . R P A T E

5 0 0 F O R M A T ( / / 1 H 1 . 4 X , ♦ W O R K I N G * . 9 X , * A V F R A G E N P V O F INC . B E N E F I T A N D I N C . 1 C O S T F O R * . 5 X , ♦ S T A N D A R D * . / 5 X , * S L 0 P E * , 1 1 X , 1 3 , ’ S I M U L A T I O N S A N D AT OI 2 S C 0 U N T R A T E OF * , F 5 . 3 , 6 X , * 0 6 V I A T I O N */)C O M P U T E T H E A V E R A G E NET P R E S E N T V A L U E OF T H E I N C R E M E N T A L B E N E F I T S A N D I N C R E M E N T A L C O S T S .OO 6 0 0 I = l . N S L O P A P V = 0.0DO 7 0 0 IS = 1 , N S I M

700 A P V = Ap V + P V ( I S , I ) 'A N P V ( I ) = A P V / N S I M 600 C O N T I N U E

C O M P U T E T H E S T A N D A R D D E V I A T I O N S OF T H E N E T P R E S E N T V A L U E S .D O S C O I = l . N S L O P SD = 0.0D O 900 IS = 1 . N S I M

900 SO = SO ♦ ( ( A N P V ( I ) - P V ( I S , I ) )**2)S T D ( I ) = S C R Tt S D / N S I M t flOO C O N T I N U E

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PRINT THE AVERAGE AMD STANDARD DEVIATIONOF MPV FOP EACH WORKING SLOPE.

DO 1000 I = 1.NSLOP 10 00 PRINT A0 0 .NWRSL(I) ,ANPV(II ,ST0 (I)400 F O R M A T (Ie,F40.0,F30.0)

STOPEND

SUBROUTINE READIM

T H I S S U B R O U T I N E RF A D S IN A L L I N P U T D A T AT H E P R O G P A M A S S U M E S THE EX I S T A N C E OF A L L T H E I N P U T D A T A .R E F E R TO THE D O C U M E N T A T I O N .N U L S L = U L T I M A T E P I T S L O P E A N G L EN S E C = N U M B E R O F S E C T O R IN T H E P I TN S L O P = N U M B E R OF W O R K I N G S L O P E S TO BE T E S T E DM A X F L = M A X I M U M N U M B E R OF F A I L U R F T H A T C A N O C C U R P E R Y E A R P E R S E C T O RN P P O D = N U M B E R OF P P Q O U C T T O N Y E A R SN Y P R = N U M B E R OF Y E A R S R E Q U I R E D F O R P R E S T R I P P I N G8 E N H T = B E N C H H E I G H TN M N P A T = B E N C H R A T T R R NNN = P R E P R O O U C T T O N P E D I O OM A X = N U M B E R O F T I M E S T R E N D IS C H A N G E DC A P A C = M I L L C A P A C I T YN S I M = N U M B E R OF S I M U L A T I O N S F O P E A C H W O R K I N G S L O P E .P R A T E = R E Q U I D E 0 R A T E OF R E T U R N .C O M M O N I O P T O , T O P T C , N U L S L , N S E C , N S L O P , N P R O O , N O N P A T ,N Y P R ,N N , 3 E N H T ,N T , 1 C A P A C ,N W R S L ( 3 > , P T O N ( 3) , C 0 S T M ( 3 , 5 ) , S T R I P R ( 3 , 3 2 ) , R A T 1 0 ( 5 ) , V O L C 5 ) , S T E ? L E V ( 5 ) , B O T P I T ( l , 5 . G D ) , O O T U L T ( 3 , 5 , 6 0 ) , P R 0 6 ( 3 , 5 , 1 0 ) , H E I T ( 1 0 ) . I T Y ° E { 5

3 , 6 0 , 3 ) , M A X , N Y ( 5 1 , P E R ( G ) ,N B U G , L H T , N P R I N T , N A M E ( 2 0 , N S I M , R R A t E C O M M O N / L I F E / N O , A N p V ( 3) ,PV( IOC, 3)R E A D 1 0 , N U L S L , N S E C , N S L O P , N T , N P R O O , N 3 N P A T , N Y P R , N N , M A X , L H T . O E N H T , C A P 1 A C , N S I M , P R A T E

10 F O R M A T ( 1 0 1 5 , 2 F 1 0 . 2 , 1 5 , F G . 3 )N W R S L ( I ) = W O R K I N G S L O p E A N G L E F O R I T H S L O P E P T O N ( I ) = P P E S T R I P P I N F T O N N A G E p O R I TH W O R K I N G S L O P E C O S T M ( I ,J) = M I N I N G C O S T p ER TON OF M A T E R I A L F O R I - T H W O R K I N G S L O P E AND J - T H S E C T O R .D O 15 1 = 1 , N S L O PR E A D 1 1 , R W R S L ( I ) , P T O N ( I ) , ( C O S T M d , J) ,.J = 1 , N S E C )11 F O R M A T ( I 5 , F 1 5 . 3 , 5 F 1 0 . 3 )S T R I P R d , IY1 = S T R I P P I N G P A T I O F O R I - T H W O R K I N G S L O P E AND J - T H S E C T O R .O N E S T R I P P I N G R A T I O IS U S E D F O R T H E E N T I R E P I T IN E A C H Y E A R . T H E R E F O R E , D I F F E R E N T S E C T O R S D O NOT H A V E D I F F E R E N T S T R I P P I N G R A T I O .R E A D 12, ( S T R I P R d , IY) , I Y = 1 , N PRO D)12 F O R M A T ( 3 ( 1 6 F 5 . 3 / ) 1

15 C O N T I N U E

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R A T I O ( J ) = R A T I O OF M I N I N G C O S T OF F A I L E D M A T E R I A L TO U S U A L M I N I N G C O S T F O R J T H S E C T O R

V O L (Jt = V O L U M E OF F A I L E D M A T E R I A L n ER T O N S T E L E V (J ) = A V E R A G E S T A R T I N G E L E V A T I O N F O R J TH S E C T O RR E A D 13, ( ( R A T I 0 C J 1 » V O L (J ) , S T E L E V (J > ) , J = 1 , N S E C )13 F O R M A T (3F1C1 .2)D O T P I T t I , J , K K ) = E L E V A T I O N O F THE R O T T O M O R T H E P I T D O T U L T (I ,J,< K) = E L E V A T I O N OF THE B O T T O M OF E X P O S E D U L T I M A T E

P I T H E I G H T NO = T O T A L L I F E OF T H E M I N ENO = NN ♦ N P & O O DO 20 1 = 1 , N S L O P D O 20 KK = 1 , N O 20 R E A D 14, ( ( n o T P l T ( I , J , K K ) ,R O T U L T (I , J ,K K ) ) ,J = 1 , N S E C )

14 F O R M A T ( 1 C F P . 21P R 0 6 (I , J , L ) = o R O B A P I L I T Y OF F A I L U R E F O R I TH S L O P E , J TH S E C T O R ,

A N D L TH W A L L H E I G H T T H I S IS I N P U T IN T H E F O R M OF A H I S T O G R A M H A V I N G AT M O S T 10 D A T A P O I N T S A N D A S S O C I A T E D F R E Q U E N C I E S .L H T = N U M B E R OF W A L L H E I G H T S F O R W H I C H P R O B A B I L I T Y OF F A I L U R E IS I N P U T T E D .H E I T ( L ) = L - T H HE IT (IN F E E T ) F O R W H I C H P R O B A B I L I T Y OF F A I L U R E IS I N P U T T E D .R E A D 1 6 , ( H F I T ( L ) , L = 1 , L H T >

16 F O R M A T ( 1 0 F 8 . 2)D O 3 3 1 = 1 , N S L O P D O 30 J = 1 ,NS FC30 R E A D 16, ( P R O B i l , J , L ) , L = 1 , L H T )C H E C K IF THE L A S T W O R K I N G S L O P E IS E Q U A L TO T H E U L T I M A T E S L O P E .IF NOT R F A D IN THE P R O B A B I L I T Y OF F A I L U R E S F O R T H E U L T I M A T E S L O P E A N G L E .I F ( N W R S L I N S L O P ) . E Q . N U L S L ) G O TO 6 5 1 = 3D O 33 J = 1 , N S E C 33 R E A D 16, ( P R O B d , J,L ) ,L = 1 , L H T )I T Y P E ( J , K K , N ) = T Y P E OF F A I L U R E F O R J TH S E C T O R , K K TH Y E A R AND N T H TI M E

65 D O 40 J = 1, N S E C DO 40 N = 1 , NT 40 ° E AO 17, ( I T Y P E (J , K K , N ) , K K = l , N O )

17 F O R M A T (6011)M I N I N G C O S T IS A S S U M E D TO C H A N G E D U R I N G T H E L I F E O F T H E M I N E .T H I S T R E N D IS E X P R E S S E D AS A T R E N D .N Y ( J J ) = Y E A R U P TO W H I C H JJ TH T R E N D IS G O O D P E R (JJ) = C H A N G E IN M I N I N G C O S T .D O 50 JJ = l . M A X 50 R E A D 1 8 , N Y ( J J 1 , P £ R ( J J )

18 F O R M A T ( I 5 , F 5 . 21

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CRtlTURNE N D

S U B R O U T I N E O U T P U TT H I S S U R P O U T I N E P R I N T S ALL T H E I N P U T D A T AC O M M O N I C P T D , I O P T C « N U L S L i N S E C t N S L O P «N P P 0 D ♦N P N P A T , N Y P R , N N , B E N H T ,N T ,

l C A P A C , N W R S L ( 3 ) , P T O N ( l ) , C O S T M ( 3 , 5 ) , S T R I P R ( 3 , i 2 ) , R A T I O ( 5 ) , V O L ( 5 ) , S T E 2 L E V ( 5 ) , n O T P I T ( T , 5 , 6 C ) , n O T U L T ( 3 , 5 , 6 0 ) , P R O H ( T , 5 , 1 0 ),H E T T ( 1 0 ) , I T Y P E (5 3 , f> 0 , 3 ) , tT A X , N Y ( S ) , P F R (5) ♦ N B U G , L H T , N P R I N T , N A M E ( 2 0 > , N S I M , R R A T E C O M M O N / L I F E / N O , A N P V ( 3) ,P V (10 C, 3)

P R I N T T H E H E A D I N G P R I N T B8 F O R M A T ( 1 H 1 . 3 5 X , * I N P U T D A T A * / / / )P R I N T 10,NAME 10 F O R M A T (10X,20AA//)PRINT 1

1 F O R M A T ( 2 X , * 1 . F I X E D V A R I A B L E S - * / / )

F I X E D D A T AP R I N T 1 1 , N U L S L , N S E C , N S L O P , N T , N P R O D , N 3 N P A T ,N Y P R ,N N , M A X ,L H T , B E N H T ,

1 C A P A C11 F O R M A T ( G X , * U L T I M A T E * , A X , * N O . O F * , S X , * N O .OF * , S X , * M A X . N O . * , 5 X , * P R O D .* 1 , 8 X ,* NO. OF O F N C H * , 3 X , * N O . O F Y R S * / 5 X , * P I T S L O c E * , 3 X ,* S E C T O R S * ,3X, 2 * W 0 R K I N G T , 3 X , * O F T Y P E * , 3 X , * L I F E OF T H E * , F X , * I N O N E * , 6 X ,* R E Q O . F O R * / 3 B X , * A N G . I N O E G . * , I X , * I N P I T * ,4 X , * S L O P E S * , 4 X , *QF. FA I L . * , 5 X , * M I N F * , A 1 C X , * P A T T E R N * , 6 X , * P P E S T R I P . * / / 1 1 0 , 1 1 1 , 2 1 1 C , 1 1 3 , 1 1 4 , 1 1 2 / / / 5 X , 5 * P R E - P R O D . * , 2 X , * M A X.NO. O F * , S X , *NO . OF H E I G H T * , 9 X , * H E I G H T * , 5 X , 6 * M I L L * / 5 X , * P E R I O D * , 5 X , * T R F N D I N * , 6 X , * F C R W H I C H * , 1 C X , * 0 F B E N C H * , 7 4 X , * C A P A C I T Y * / 5 X , * I N Y D S * ♦ 5 X ,* MIN I N G C O S T * , 3 X , * P R O D . F A I L . * , 9 X ,8 * 1 N f f e t * , 5 X , * T O N S / D A Y * / 3 0 X , * I S K N C W N * / / 1 9 , 1 1 2 , 1 1 5 , F 2 0 . 1 , F 1 2 . 1 / / / ) P R I N T 6 , N S I M . R R A T E

6 F O R M A T ( 5 X , * N U M 3 E R 0 F * , 5 X , * R A T E OF * / 5 X , * S I M U L A T I O N S * , 3 X , * RE T U R N *// I I 11 , F 1 2 . 3///T P R I N T 2

2 F O R M A T ( 2 X , *2. P R E S T R I P P I N G T O N N A G E A N D M I N I N G C O S T S - * / / )

V A R I A B L E D A T A P R I N T 12

12 F O R M A T ( 5 X , * W 0 R K . S L 0 P E * , 7 X , * P R E - S T R I P . * , 1 G X , * M I N I N G C O S T F O R S E C T O R 1 * / , 8 X , * A N G L E * , 1 1 X , * T O N N A G E * , 8 X ,*1 2 3 4 5 *2/)DO 20 I = 1 , N S L O P

20 P R I N T 13, N W R S L C I ), P T O N t l ) , ( C O S T M d , Jl , J = 1 , N S E C )13 F O R M A K I 1 1 , F 2 1 . 0 , 1 X , 5 F 8 . 3 )P R I N T 3

3 F O R M A T ( / / / ? X , * 3 , S T R I P P I N G R A T I O S - * )

69

P R I N T q , N P R O O9 F O R M A T f / / / 9 y , * W 0 R < . S L O P E * , 29X, *ST R I P P I N r , R A T I O S F O P P R O D U C T I O N Y E A 1 R S * / S X , * A N G L E * , 3 2 Y , *1 T H R O U G H * ,13)00 30 I = 1 , NSL OP30 P R I N T 1 L , N W R S L ( I ) , ( S T R I D R ( I , I Y ) ,IY = 1 , N P R 0 0 )

14 F O R M A T </ 1 1 1 , 5 X , I b F b . 2 / 1 6 X , 1 6 F 6 . 2 / l 6 X , 1 6 F 6 . 2)PPI NT 44 F O R M A T (Z / / 2 X , *4. R A T I O , V O L U M E , A N D S T A R T I N G E L E V A T I O N - * )P P I N T 1915 F O R M A T ( / / / 5 X , * S E C T OR*, 5 X , * R A T I O * , 5 X , * V O L f T O N * , 5 X , * S T A R T .E L E V .*/) DO 50 J = 1 , N S E C50 P R I N T 15, J , R A T I O ( J ) ,VOL (J) , S T £ L E V ( J)16 F O R M A T ( I 9 , F 1 2 . 2 , F 1 0 . 1 , F I 7.11P R I N T 55 F O R M A T ( / / / 2 X , *5. E L E V A T I O N S O F P I T Q O T T O K A N D B O T T O M OF THE E X P O S E

10 U L T I M A T E P I T - * / / 3 C X , * P O T P I T = B O T T O M OF T H E P I T * / 3 u X ,* B O T U L T = 2 B O T T O M OF THE E X P O S F D U L T . P I T *1DO 60 I = 1 , NSL OP P R I N T 1 7 , N W R S L ( I )17 F O R M A T ( / / / 5 X , * W O R K I N G S L O P E = * , I 3 / / 5 X , * Y E A R * ,9 X ,* S E C T O R 1 * , 8 X , * S E 1 C T O R 2 * , 8 X , *S E C T OR 3 * , A X ,* S E C T OR 4 * , 8 X , * S E C T Q R 5 * / 1 5 X ,* B O T P I T * 2 X ,*

2 B O T U L T * , 2 X , * B 0 T P T T * , 2 X , * B O T U L T * , 2 X ,* B O T ° I T * 2 X , * B O T U L T * , 2 X , * 9 0 T P I T * 3 , 2 X , * B 0 T U L T * 2 X ,* B 0 T P I T * . 2 X , * D 0 T U L T * / )D O 60 KK = 1 , NOP R I N T lfi,KK,( ( D O T P I T ( I , J , K K > , B O T U L T (I , J , K K ) 1 , J = 1 , N S E C )16 F O R M A T ( 1 8 , 5 X , 1 0 F 8 . 11

60 C O N T I N U E P R I N T 9191 F O R M A T ( / / / 2 X , * 6 . H E I G H T O F W A L L - * )P R I N T 21, ( H E I T ( L ) , L = 1 , L H T )

21 F O R M A T ( / / / 5 X , * H E I G H T S F O R W H I C H P R O Q . OF F A I L U R E IS I N P U T T E D C I N F T 1 . ) * / / 5 X , 1 0 F 3 . 2 / IP R I N T 77 F O R M A T ( / 2 X , *7. P R O B A B I L I T Y OF F A I L U R E - * )DO 70 I = 1 , NSL OP P R I N T 2 2 , N W R S L (I )22 F O R M A T < / / 5 X , * W 0 R K I N G S L O P E = * , 1 3 / 1 P R I N T 2 3 , L H T

23 F O R M A T ( 5 X , * S E C T 0 R * , 5 X , ♦ P R O B A B I L I T Y OF F A I L U R E S W A L L H E I G H T S 1 T H R O 1 U G H * I 3/1D O 70 J = 1, N S E CP R I N T 25, J, (PROI3(I,J,L) ,L = 1 , L H T )25 F O R M A T ( I 9 , 5 X , 1 0 F 6 . 3 )

70 c o n t i n u eI F ( N W R S L (N S L O P ) . E O . N U L S L ) G O T O 52 P R I N T 5 3 , N U L S L ,L H T

53 F O R M A T ( / 5 X , * N O T E - L A S T W O R K I N G S L O P E IS N O T E Q U A L TO T H E U L T I M A T E1 S L O P E A N D H E N C E T H E * / l 2 X , * ° R n D A G I L I T Y OF F A I L U R E F O R T H E U L T I M A T E2 S L O P E IS I N P U T T E D S E P E R A T E L Y *//3 5 X , * U L T I M A T E S L O P E A N G L E =* I 3 / / 5 Y , * S E C T 0 » * , 5 X , * P P Q B A B I L I T Y OF F A I L 4 U R E S F O R W A L L H E I G H T S 1 T H R O U G H * , 13 / )1 = 3D O 54 J = 1 , N S E C

54 P R I N T 2 5 , J , ( P R O f l C I , J , L ) , L = 1 , L H T )52 P R I N T 3131 F O R M A T ( / / 2 X , *8. T Y P E S O F F A I L U R E - * / )

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D O 80 I = 1 * K'SEC PRINT j2,J

32 FORMAT(/5X,*SECTQ9»,13/)P R I N T 33

33 FORMAT(5Y,*TIMF*5X,*TYPES OF FAILURE FOR EACH YEAR OF LIFE*/)OU HO N = 1 « NTP R I N T 3A , N , ( I T Y P E ( J , K K , N > , K < = 1,N D)

34 FORMAT(IP,3X,6012/)80 C O N T I N U E

PRINT 3635 FORMAT(//2X,*q. TREND DATA f0R MINING COST-*//5X,*YEAR*,5X , *TREND ♦

1/)DO 90 JJ = 1 , M A X 90 P R I N T 3 6 , N Y (J J ) , P F R ( J J )36 FORMAT(I8,F11,2)

RETURNEND

S U B R O U T I N E B E N E F lT H I S S U B R O U T I N E C O M P U T E S P R E S T R I P P I N G C O S T S f q R E A C H P R E P R O O U C - TI ON Y F A P S AND S T R I P P I N G C O S T S F O R E A C H P R O D U C T I O N Y E A R S F CR E A C H W O R K I N G S L O P E A N G L E S . C A L L S U S E R S U P P L I E D B E N E F I T R O U T I N E (IF ANY) TO C O V E R O T H E R B E N E F I T S . S A V I N G S IN S T R I P P I N G C O S T IS C O N S I D E R E D AS B E N E F I T . A N N U A L I N C R E M E N T A L B E N E F I T S APE C A L C U L A T E D W I T H R E S P E C T TO THE F I R S T C A S E W H I C H IS T H E B A S E C A S E .N S L = N U M B E R OF P R E P R O D U C T I O N Y E A R S IN W H I C H S T R I P P I N G H A S N O T BEEN S T A R T E D .N P L = F I R S T Y E A R OF P R E S T R I P P I N G M H L = F I R S T P R O D U C T I O N Y E A R NO = T O T A L L I F E IN Y E A P SA R S T P ( I ) = A M O U N T OF P R E P R 0 0 U d I O N S T R I P P I N G PER Y E A R F O R I - T H

W O R K I N G S L O P EC O M M O N I O P T B , I O P T C , N U L S L , N S E C , N S L O P . N P R O n , N B N P A T , N Y P R , N N , B E N H T , N T ,

1 C A P A C , N W P S L ( 3 ) . P T O N ( 3 > , C O S T M ( 3 , 5 ) , S T R I P R ( 5 , 3 2 ) , R A T 1 0(5) , VOL ( 5 ) , S T E 2 L E V ( 5 ) , B O T P I T ( 3 , 5 , 6 0 » , B O T U L T ( 3 , 5 , 6 0 ) , P R O P ( 3 , 5 , 1 0 ) , H E I T (10) , I T Y P E ( 53 , 6 0 , 3 ) , M A X , N Y ( 5 > , P E R ( 5 ) , N P U G , L H T , N P R I N T , N A M E (20) , N S I M , R R A T E C O M M O N / R A J / A R S T P ( 3 ) , 8 E N S T ( 3 , 6 C ) , B E N O T ( 3 , 6 0 ) , B E N I N ( 3 , 6 0 ) , X C O S T ( 3 , 6 0 1)C O M M O N / T P E N / C O M N (3,5,60) , A C O S T (60)NSL = NN - NYPR NPL = NSL + 1 MPL = NN + NPROD NO=NN+NPROD

INITIALIZE THE ARRAY VARIABLES.

DO 80 I = 1,NSL OP ARSTP(I) = 0.0 DO 80 KK = 1 ,NDBENST(I,KK) = 0 . 0 ARENOT(T,KK) = 0.0 BENIN(I,KK) = 0.0 XCOST(I,KK) = 0.0

80 CONTINUE

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DO 10 1 = 1 , N S L 0 PC O M P U T E T H E A V E R A G E M I N I N G C O S T F O R E A C H W O R K I N G S L O P E . THE A V E R A G E M I N I N G C O S T TS D E F I N E D AS THE A V E R A G E V A L U E OF THE M I N I N G C O S T S F O R ALL THE S E C T O R S .M A X = NUM'JFR OF T I M E S T H E T R E N D IN C H A N G E O F M I N I N G C O S T IS C H A N G E D .I F ( N Y ( M A X ) . L T . N O ) GO TO 65 I F ( N Y ( M A X ) . G T . N O ) N Y ( M A X ) = ND G O TO 75 65 M A X = M A X ♦ 1 N Y ( M A X ) = NO P E R (MAX) = 0.0

75 LL = 1D O 5 JJ = l . M A X DO 11 KK = L L , N O C O S T = 0 . 0T F ( K K . G T . N Y C J J ) ) G O TO 23 I F (K K . G T ,1) GO T O 19 PE = 0.0 GO TO 9 19 PE = P E R (J J )9 DO 16 J = l . N S F C I F ( J J . G T . l ) GO TO 27 C = C O S T M (I ,J)KM = K<G O TO 24 27 C = C O M N ( I , J , M M )JT = JJ - 1 KM = KK - N Y ( J T )24 C O M N (I ,J , K K ) = C * ( ( 1 + P E ) * * K M )

16 C O S T = C O S T + C O M N ( I , J , K K )A C O S T ( K K ) = C O S T / N S F C

11 C O N T I N U E 23 MM = KK - 1 LL = N Y (JJ) +15 C O N T I N U EA R S T P ( I ) = P T O N ( I ) / N Y P RP S C O S T ( I , KK) = P R E S T R I P P I N G C O S T F O R K K - T H Y E A R OF THE T O T A L L I F E AND I - T H W O R K I N G S L O P E .S T C O S T (I , KK) = S T R I P P I N G C O S T F O R K K - T H Y E A R OF THE T O T A L LIF E

AND I - T H W O R K I N G S L O D £.O E N S T (I , KK) = B E N E F I T F O R M L E S S S T R I P P I N GD O 33 KK = 1 , N N I F ( K K . G E . N P L ) GO T O 6 P S C O S T = 0.0 G O TO 7

6 P S C O S T = A R S T P ( I ) * A C O S T ( K K )7 X C O S T (I , K K ) = P S C O S T 30 C O N T I N U E

D O 40 IY = 1 , N P R O D K K = IY + NNS T C O S T = C A P A C ♦ S T R I P R ( I , I Y ) * A C O S T ( K K ) * 350 X C O S T ( I , K K ) = S T C O S T

40 C O N T I N U EC I F ( I . G T . l ) GO TO 15

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n o 53 KK = l . N O 50 H C M S T ( I , K K > = 0.0 G O TO 1 uC

15 no GO k k = l. N TBF.NST ( I ,KK) = XCOST (1»KK) - XCOST ( I, KK)

60 CONTINUE 10 CONTINUE

CHECK IF THFPE IS A USER SUPPLIEO BENEFIT ROUTINE

B E N O T (I.KK) = O T H E R BENEFIT SUPPLIED B Y USER

IF(IOPTB.EO.1) GO TO L5 00 35 1=1.MSLOP DO 35 KK=1,NO

35 BENOT(ItKKI = 0.0 G O TO 47C A L L U S E R S U P P L I E D B E N E F I T R O U T I N E TO C O V E R A N Y O T H E R B E N E F I T S . T H I S R O U T I N E IS C A L L E D O N L Y O N C E .

45 C A L L B E N E F 247 D O 55 1 = 1» N S L O P

D O 55 .KK = 1« NO 55 B E N I N ( I . K K ) = B E N S T t I . K K ) ♦ B E N O T ( I . K K )B E N I N ( I . K K ) = T O T A L I N C R E M E N T A L B E N E F I T S F O R N O N B A S E C A S E .R E T U R N .E N D

S U B R O U T I N E P R O B F L ( I , J . K K , W A L L )T H I S S U B R O U T I N E C O M P U T E S T H E C U M M U L A T I V E P R O B A B I L I T Y D I S T R I B U T I O N A N D F I N D S OUT W H E T H E R O R N O T T H E R E IS A F A I L U R E F O R A S E C T O R IN A G I V E N Y E A R .C O M M O N l O P T B . I Q P T C . N U L S L . N S E C , N S L O P ,N P P O D . N B N P A T , N Y P R .N N .B E N H T .N T ,

1 C A P A C , N W P S L (3) , P T O N ( 3 ) . C O S T M ( 3 . 5 ) , S T R I P R ( 3 . 3 2 ) . R A T I O ( 5 ) , V O L ( 5 ) , S T E ? L E V (5) . B O T P I K 3,5 , 60 ) . 3 0 T U L T ( 3 , 5 , 6 0 ) , P R O B ( 3 , 5 , 1 0 ) , H E I T ( 1 0 ) , I T Y P E ( 53 , 6 0 , 3 ) . M A X , N Y ( 5 ) . P E R (51 . N B U G . L H T , N P R I N T , N A M E ( 2 0 1 . N S I M . R R A T E C O M M O N Z R P U / P F A I L ( 3 , 5 , 6 0 ) , N F A I L ( 3 , 5 , 6 0 )I N I T I A L I Z E THE A R R A Y V A R I A B L E S .P F A I L ( I , J , K K ) = 0.0 N F A I L d , J . K K ) = 0F I N D O U T T H E P R O B A B I L I T Y O F F A I L U R E F O R G I V E N W A L L H E I G H TP F A I L ( I , J . K K ) = P R O B A B I L I T Y OF F A I L U R E F O R I - T H W O R K I N G S L O P E ,J - T H S E C T O R A N D K K - T H Y E A R .N F A I L ( I , J t K K ) = IF E Q U A L S 0 NO F A I L U R E , IF E Q U A L S 1 F A I L U R E .IF ( W A L L •G T .0.) G O TO 52

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G O TO 82 52 00 ^0 L = i »LHT HT = H E I T ( L )I F ( W A L L . L T . H T ) GO TO 55 G O TO 63

55 m = l -1PFAIL(I,J,KK) = P ? 0 9 ( I , J , M ) 4 ( ( (P900(I , JtL) - P R O B ( T « v (WAL

1L - HF.IT(M) n / ( H E I T ( L ) - H E I T ( M ) ) )P F = PPAIL ( I«J,KK)G E N E R A T E R A N D O M N U M B E R A N D F I N D OUT* W H E T H E R OR N O T T H E R E IS A F A I L U R EX = R A N R ( C)I F ( y . G T . P F ) GO TO 82 N P A I L d , J , K K > = 1 G O TO 82

60 C O N T I N U E 82 R E T U R N E N D

SUBROUTINE COST1

THIS SUBROUTINE CALLS PROBFL TO FIND OUT WHETHER OR NOT THRRE IS A FAILURE AND DEPENDING UPON THE TYPE OF FAILURE CALLS APPROPRIATE ROUTINE TO COMPUTE COSTS

DIMENSION WALHT(3,5,60),ULTHT(3,5,60)COMMON IOPTB,IOPTC,NULSL,NSEC,NSLOP,NPROD,N0N°AT,NYPR,NN,9ENHT,N T ,

ICAPACtNWOSL(3),PT0N(3>,COSTM(3,5),STRIPR(3,32),RATIC(5),V0L(5),STE 2LEV(5),BO TP IT(3,5,60), BOTULT(3,5,60),PROB(3,5,1 0 ) , HEIT(10), I TV PE (53,60,3),MAX,NY(5),PER(5) ,NBUG,LHT,NPRINT,NAME(20) ,NSIM,RRATE COMMONXRPU/PFAIL(3,5.60) ,NFAIL (3,5,60)COMMON/EMA/FCOST(3,5,6C),OTCGST(3,5,60),TCOST(3,5,60),COSTN(3,5,60

1),COST I N (3,60) .FFCST(3,60),TOCST(3,60) ,TCT(3,60)

N O = N N + N P R O DI N I T I A L I Z E THE A R R A Y V A R I A B L E S .D O 122 I = 1 , N S L OP D O 1 2 2 J = 1 , N S E C D O 122 KK = 1 , NO F C O S T d , J , K K ) = 0.0 O T C O S T ( I , J , K K ) = 0.0 T C O S T ( I , J , K K ) = 0.0 C O S T N ( I ,J ,KK) = 0.0

122 C O N T I N U ED O 1 2 5 I = 1 , N S L O P DO 1 2 5 KK = 1 , N O C O S T I N d ,KK) = 0.3 F F C S T ( I , K K t = 0.0 T O C S T ( I ,K K ) = 0.0 T C T ( I . K K ) = 0.3

125 C O N T I N U EDO 30 1 = 1 , N S L O P D O 30 J = 1 , N S E C

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74

C O M P U T E E N T I R E W A L L H E I G H T A N D W A L L H E I G H T F O R E X P O S E D U L T I M A T E P I T L I M I TS T E L E V ( J ) = A V E R A G E S T A R T I N G E L E V A T I O N OF J - T H S E C T O R .W A L H T ( I ♦J , K K ) = C O M P U T E D W A L L H E I G H T F O R T H E P I T W I T H I - T H W O R K I N G

S L O P E , J - T H S E C T O R AND K K - T H Y E A R .U L T H T ( I , J . K K 1 = C O M P U T E D H E I G H T O F T H E E X P O S F O U L T I M A T E P I T W A L LF O R I - T H W O R K I N G S L O P E , J - T H S E C T O R A N D K K - T H Y E A R .D O 40 K K = 1 , NO IT = 0WALHT(I,J,KK» =STFLFV(J) - ROTPIT(I ,J tK K )U L T H T ( I , J , K K ) = S T E L F V C J ) - D O T U L T ( I . J . K K )IT IS A S S U M E D T H A T T H E ° U S H B A C K IS L A R G E E N O U G H T O C O N S I D E R T W O D I F F E R E N T H E I G H T S F O R S A M P L I N G F O R F A I L U R E . C N L Y O N E P U S H B A C K IS A L L O W E D AT A T I M E .I F ( K K . G T . l ) GO TO 500 W A M M = W A L H T ( I . J . K K )H3 = 0.0 GO TO 6 1 1

5 0 0 KT = KK - 1W A M M = W A L H T ( I . J . K K )D O 5 0 5 KT T = l . K T W A T T = W A L H T t l , J . K T T )I F ( W A M M . L T . W A T T ) G O TO 506 G O TO 5 0 5 5 0 6 W A M M = W A T T

5 0 5 C O N T I N U EH3 IS T H E H E I G H T OF THE W A L L B E L O W THE P U S H B A C K .H3 = W A M M - W A L H T ( I . J . K K )

6 1 1 C A L L P R O B F L d , J . K K . H 3 )IT = IT + 1NF = N P A I L ( I . J . K K )I F ( N F . G T . O ) GO TO 6 0 6 C F 1 - 0 . CC A L L S U B R O U T I N E P R O B F L TO F I N D O U T W H E T H E R OR N O T T H E R E IS A F A I L U R E

6 0 7 W A L = W A L H T ( I . J . K K )6 0 8 C A L L P R O B F L d , J . K K , W A L )IT = IT ♦ 189 NF = N F A I L ( I . J . K K )

I F ( N F . G T . O ) GO TO 90 C F 2 = 0.0G O TO 140C H E C K T H E TY P E OF F A I L U R E A N D C A L L A P P R O P R I A T E R O U T I N E TO C O M P U T E THE C O S T

6 0 6 WAL = H 390 W A L M = W A L G O TO 7875 W A L M = U L T H T C I ,J . K K)

75GO TO 512

CC NT = N U M B E R OF T Y P E S OF F A I L U R E T H A T A S E C T O R C A N H A V E .C 78 I F ( I T . E O . 1) GO TO 512IF (IT. £ 0 . 3 ) GO TO 512CC IN C A S E S W H E R E T H E R E IS K I N K IN T H E S L O P E . U P P E R P O R T I O N ( U L T I -C M A T E S L O P E ) IS N O T S A M P L E D IF THE F A I L U R E IN T H E L O W E R ( W O R K I N GC S L O P E ) IS A L A O G E F A I L U R E .C 0 0 511 N = 1 , NT

I F ( I T Y P F t J . K K . N ) . G T . 2) GO TO 5 1 0511 C O N T I N U E L F A I L = C G O TO 5125 10 L F A I L = 1512 CF = 0.000 50 N = 1 . NT

I F ( I T Y P E ( J . K K . N ) . £ 0 .0) GO T O 2 3 0G O T O C S I . 9 2 . 9 3 . 9 4 ♦ 9 5 . 9 6 . 9 7 I . I T Y P E ( J , K K ♦N>91 C A L L F C O S T 1 ( F A I L C )G O TO 24092 C A L L F C 0 S T 2 ( I . J . K K . F A I L C )

G O TO 24 093 C A L L F C O S T 3 ( I , J . K K . W A L M . F A I L C )G O TO 24094 C A L L F C 0 S T 4 G O TO 24095 C A L L F C O S T 5

GO TO 24096 C A L L F C 0 S T 6 G O TO 240

97 C A L L F C O S T 7 G O TO 240230 F A I L C = 0.0 240 CF = CF + F A I L C 50 C O N T I N U E

I F ( I T . E O . l ) GO TO 5 1 5 I F ( I T . E 0 . 2 ) GO TO 605 CF 3 = CF G O TO 5 1 8

5 1 5 C F 1 = CF G O TO 6 0 7

6 0 5 C F 2 = CFI F ( L F A I L . G T . 0 ) GO TO 7CC C H E C K IF T H E RE IS E X P O S E D P I T L I M I T

C 140 I F ( U L T H T ( I . J . K K ) . G T . 0 . 0 ) G O TO 77G O TO 777 I F ( N W R S L ( N S L Q P ) . N E . N U L S L ) G O T O 4 1 0 G O T O ( 1 . 2 . 3 ) ♦I1 I I = I + N S L O P - l

G O TO 42 I I = I + N S L O P - 2 G O TO 43 I I = I + N S L O P - 3 G O TO 44 1 0 II = 3

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76U ULT = ULTHT(I,J,KKI

CALL P^ORFL TO FIND OUT IF THERE IS A FAILURE IN THE EXPOSED ULTIMATE PIT LIMIT

CALL PROBFLCII«JtKK,ULT)IT = IT + 1 14 I F ( M F A I L ( I I » J , K K ) . G T . O ) GO TO 75

7 C F 3 = 0.0 5 1 8 F C O S T (I. J t K K t = C F 1 f C F 2 «• CF 3OTCOST(ItJtKK) = OTHER COSTSTCOST(It JtKK) = TOTAL COSTCOSTN(I ,J *KK) = INCREASE IN COST CQR I-TH WORKING SLOPE* J-TH

SECT00 AMD KK-TH YEARCOSTIN(I,Jt KK) = INCREMENTAL COST

CHECK IF THERE IS ANY OTHER COST

IF(IORTC.GT.O) GO TO 110 OTCOST(I *Jt KK) = 0.0 GO TO 120

CALL USER SUPPLIED COST ROUTINE

110 CALL C0ST2120 T C O S T (It JtKK) = F C O S T (I , J, KK ) «- O T C O S T < I » J * KK)

I F ( I . G T . l ) GO TO 130 C O S T N d t JtKK) = 0.J G O TO 40130 C O S T N d , J,KK) = TC OS T (I * J t KK ) - T C O S T (1* JtKK)

40 CONTINUE 30 CONTINUE

COMPUTE THE COST OF FAILURE * OTHER COSTS AND TOTAL COSTS F CR I-TH WORKING SLOPEt AND KK-TH YEAR.FFCST(It KK) = COST O^ FAILURE FOR I-TH WORKING SLOPE AND KK-TH

YEAR.' TOCST (It KK) = OTHER COST FOR I-TH WORKING SLOPE AND KK-TH YEAR.

TCT(I,KK) = TOTAL COSTS FOR I-TH WORKING SLOPE AND KK-TH YEAR.

OO 4 0 0 I = l . N S L O P D O 4 0 0 KK = l,Nf)CC = 0.0C F F = 0.0DO 302 J = 1.NSECCFF = CFF + F C O S K I, J,KK>CC = CC + OTCOST(1.JtKK)302 CONTINUEFFCST(ItKK) = CFF TOCST(ItKK) = CCTCT(I,KK) = FFCST(ItKK) + TOCST(I,KK)400 C O N T I N U EA D O INCREMENTAL COST OF EACH SECTOR

D O 200 1 = 1 1 N S L O P D O 200 KK = 1 «ND C O S T P T = 0.0

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D O 30C J = l , M S E CC O S T 0 T = C O S T P T ♦ C O S T N C I , J , K K ) 3 00 C O N T I N U EC 0 S T I N ( I , K K ) = C O S T P T 200 C O N T I N U E R E T U R N

E N D

SUDROUTIIIE F C O S T K F&ILC)

THIS SUHPOUTINE ASSUMES THAT THE COST OF FAILURE IS ZERO.

FAILC = G.GRETURNE N D

SUBROUTINE FCOST2(I.J,KK,FAILC>

THIS SUBROUTINE COMPUTES THE COST OF FAILURE WHERE THE FAILURE IS OF TYPE 2. IT IS ASSUMED THAT THE CLEANING IS DONE BY THE COMPANY. COST OF CLEANING / TON OF MATERIAL IS SAME AS THE USUAL MINING COST.

COMMON IOPTB.IOPTC.NULSL.NSEC.NSLOP.NPROD.NBN°AT tNYPR.NN.BENHT.NT. 1CAPAC.NWPSL(3).PTONC3) , COSTM(3.5) , STRIPR(3.32>.RAT 10<5>.VOL(5) .STE 2LEV<5>.BOTPIT<3,5,6G).BOTULT(3,5,6 0),P ROB(3,5,10),HEIT(10) ,ITY°E(53,60,3).MAX,NY(5) .PER(5) ,NBUG,LHT.NPRINT.NAME(20) .NSIM.RRATE COMMON/TREN/COMN(3,5,6 0),ACOST(60)

FAILC = ((0.0%*((3ENHT*NDNPAT)**3))*COMN(I,J,KK))/VOL(J)RETURNE N D

SUBROUTINE FC0ST3(I,J . K K , WALL,FAILC)THIS SUBROUTINE CALCULATES THE COST OF FAILURE WHERE FAILURE IS OF TYPE 3. TYPE 3 FAILURE DOES NOT INCLUDE ANY RAMP

C O M M O N l O P T B . I O P T C . N U L S L . N S E C , N S L O P . N P R O C , N O N F A T , N Y P R . N N . B E N H T , N T , 1C AP AC ♦ N W R S L (3) , P T O N ( 3) , C O S T M (3 , 51 , S T R I PP. ( 3 , 3 2) , R AT I O (5 ) , V 0 L ( 5 ) , S T E 2 L E V (5) ,f)GTPIT ( 3, 5, 60 ) . B O T U L T (3,5, 63 ) , P P O R ( 3 , 5 ♦ 1 0 ) , H E IT (10 ) , IT Y P E (5 3 , 6 0 , 3 1 , M A X , N Y ( 5 ) . P E R ( 5 ) . N R U C . L H T , N P R I N T . N A M E ( 2 0 ) , N S I M . R R A T E C O M M O N / T R E N / C O M N ( 3 , 5 , 6 0 ) , A G O S T (60)F A I L C = ( ( 0 . 0 8 * ( W A L L * * 3 ) I * R A T I O ( J ) * C O M N ( I , J , K K ) ) / V O L ( J )RETURNE N D

SUBROUTINE NETPV(IS)

THIS SUBROUTINE COMPUTES THE NET PRESENT VALUE OF THE INCREMENTAL BENEFIT AND INCREMENTAL COST)

78

COMMON I O P T n , I O P T C , N U L S L , N S E C , N S L O P , N P R O O , N R N P A T , N Y P R , N N , n F N H T , N T , I C A P A C t M W R S L ( ) l , P T O N ( 3 ) , C O S T M ( 3 , 5 ) , S T R I P 3 ( 3 , 3 2 ) , R A T I O ( 5 ) , V O L ( 5 ) , S T E 2LEV ( 5 ) , J C T P I K 3 , 5 ♦ r>: ) . f JOTULT ( 3 , 5 , 6 3 ) , PROR ( 3 , 5 , 1 0 ) , H E I T ( 1 0 ) , I T Y P E ( 53 , 6 0 , 3 ) , M A X , N Y ( 9 l , P E R ( 5 ) , NRUG , L H T , ,NP» I N T , NA I E C ? 0 ) , N S I M ♦ P R ATE

C 0 M M 0 N / R A J / A R S T P ( 3 ) . " E N S T ( 3 , f 0 ) , P E N O T ( 3 , 6 0 » , R E N I N ( 3 ♦ 6 0 ) , X C O S T ( 3 , 6 0 1)

COMMON/ EMA/ FCO S T ( 3 , 5 . 6 0 ) , 0 T C O S T ( 3 , 5 , 6 3 ) t T C O S T ( 3 , 5 , 6 C ) , C O S T N ( 3 , 5 , 6 0 1 ) . COST I N ( 3 , 6 0 ) . F F C S T ( 3 , 6 0 ) . T O C S T ( 3 « 6 0 ) . T C T C 3 . 6 0 )

C O M M O N / L I F E / N O , A N P V ( 3 ) , P V ( 1 3 0 , 3 )

DO 10 T = l . N S L O P PVB = 0 . 0PVC = 0.0DO 20 KK = 1 ,NOP V R = P V B + ( B E N T N d .KK) ♦ (1/ ( ( 1 + R R A T E ) * * K K ) ) )PVC = PVC + ( C O S T I N d . K K ) * ( 1 / C ( H - R R A T E I * * K K ) ) 1

2 0 CONTI NUEP V ( I S , I ) = PVB - PVC

10 CONTI NUE RETURN END

APPENDIX CINPUT DATA AND OUTPUTS OF THE BENEFIT COST MODEL

7.9

hkRUlUAL HIRING COMPANY OK CANADA

F1XEU vMKiABLE

Uu TIHa Iu N O .OK f.O.OF MAX,NO. PROD. NO.Of- BcN<Pi] SuvK't: SEu TUKS WORKING OK TYPE LIKE OK THl IN U'N-AiiO.Ii- Ui-b. IN PIT SLOPl B OK FAIL. MINE Pa TTEk N

45 . a 2 1 25 1

Pkc-PkOD. NAX.NU.OF K'EklCu Tr\ENL INii\ YrsO NiNINu COST

NO.OK HEIGHT FOR WHICH PRCB.FAIL.15 KNOWN

HEIGHT OF BENCH IN FEET

MILLc a p a c i t yTO.jS/u a Y

10 40.0 ;5ooo. c

NUMuEH OF KATE OKSIMULATIONS RETURN

100 .150

PivLSTruPPiUG TONNa GE AND MINING C05TS-

WOr K.Su OPc. ‘ PRE-STRIP. MINING COST FOR ScCTCRAinvuE TONNAGE 1 2 5 4

NO.OF YRS RECO.FUR pRCSTxiP,

3

2333

910C00CU. .230 ,23065b^u0o0. .250 .250

j, bl MHhif.v KaT lub*

WuAik.buOPc. S T R I P P I N G RAT I O S FOR P R O D U C T I O N Y^ARSA u v w E; 1 T H R OUGH 255.52 5.52 5.52 2, cl 2.til 2.61 2.81 2.61 2.81 2,til 2.49 2.49 2.49 2.49 1.61 1.61l.bl l.ul 1.61 l.ul .53 .53 .53 .53 .534.29 4.29 4,29 2.26 2.2b 2.2ft 2.2b 2.2ft 2.2b 2.26 3,04 3.04 3.04 3.04 1.61 1.611 « b 1 1 ebl 1.61 l.ul 1.43 1.43 1,43 1.43 1.43

4. KAlIOf VOuui<iA«jD START uNO LLtVATlOiN-

Sl c i u k r a t i o v c l / t o n s t a r t ,e l e v .1 l.cb 12,0 bSOO.O<; 1,2b 12.0 5900.0-

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t>. L L l Va ) iONo OK Pi T uO i TOM AND WOT] OK Or TiiE E A P O S l U U L T IMATE KlT"bOTPiT = B O T I V M OK THE PITLUTULT = bOI TOM OF THE EX P O S E D ULT. PIT

r.VKKlho buvKE = 2b Yl AH U c C T O A 1 bLCTQR 2

vOlPiT nOTUuT VOTP1T liOfvLT1 uSUO.u bbVu.0 5900.0 590 0.0c uSUO•0 o50u.0 5900.0 S50J.00 oSUj,0 0500.0 d90U.O 5900.04 tiSOO • U 0500.0 5900.0 59UU.0S vbU).u 0500,0 5900.0 590v.Ou SObO•0 bOvu . 0 b9uu.O 5900.07 b 7 u o , u 6000.0 59uu.O 590 0.0u uStij, u UPbO.O 59u0.0 590u.Oy S4ou•0 Cli-O.O 59uu.0 59uu,0

10 • O0t>0. U bl4U,0 5900.0 590u.OAi dOGO.U olvU.O 5900.0 590u.Olb jobJ,0 SOuu. 0 5900.0 5900.010 b4bij . 0 60bU,0 5900.0 S9uu,0

bOuj•0 5900.0 59u0.0 5900.0IS 01 o.j , 0 5940.0 5900.0 590u . 0lo SluJ.O 59uL,0 5ho0•0 590u.Oa7 UlGO.U Srtoo,0 570 0.0 Sfsuu. (jId L)UbO . U. 5620,0 554u.O 5820.0iy SOoO•0 bVcU.O 5JoO.0 57du,0bO SObO.U 5740,0 52b0,0 574 0.0bi bObO.U 5 / u u , U bloo.O 57Ou, 0cd h 9o O •0 Sbdo.O 4 960.0 Sftou.0cu bOUO.O SfcbU.O 5300. 0 56b0.024 uloO, U 5Sou,0 52b0.3 55JO•0bS S1U lj . U 55‘tu, 0 5140.0 5540.0bo dUbfJ. U 5y00,0 ddoo.0 5500.0b7 4940.u S'+uO, 0 50411.0 54t->o , 0bo 4900.0 54du,0 4 960.0 b-toG * 0

JtibO.O 5dOu. 0 5020.0 550u,0Ou 49dU.O 5140,0 49o0.0 "5140.001 4R'*u.O SOt-U, 0 494u ,0 L-02u • 0Ob 4900,0 4940.0 4900.0 4940.000 4buJ,0 46uu,0 49Uu .O 4 9 0 u , 0

SECTOR i SECTOR 4P O T PIT DOTULT 2 0 1 PiT BOTULT SEC TOR 5 R O T k i t tJOTULT

oots)

wCKKihu SuUPc = jb

SvCTUH 1 bLCTCf' '<LoClPiT b o t u l t bOTPIT rOTuLT

1 oSO J.0 CbOo.O 5900.0 5900.02 obU j.0 bbUU.O 5900.G 5900.00 Obuj.u 6b00,0 5900.0 5900.04 ubuo.0 CbOO.O 59uU.O 590u.0b obO(), 0 6b0u.0 5900.0 5900.0u She.). 0 obOO.C S9UU.0 59Oo•07 S7U0.U hbUO,0 590o •0 5900.0ti bboj.O 6400.0 59Ou,0 5900.09 b4u.),U 6400,0 5900.0 5900.0

lu u J JO , li 64vu,0 5900.0 59UO.011 Sbuj, 0 64u0,0 59U0.0 590 0.012 bbuo.G o42U.U 5900.U 5900.013 JboO.O 6 j 3 0 .0 5900.0 590o , 014 bcou.O 6340,0 56u0.0 5902.0lb bidu.o 6300.0 5900.0 59OC.0lt> blUO.O 62v0,0 5900.0 590 0.017 bOo.j.b 62cu,0 5900.0 5900,3lo s 0 2 0 • 0 62co.0 5900.0 590u.OiV ‘♦Uo ). 0 occO.O btloO • 0 59Uu.0cU S3uu.0 6140.0 5700.0 5900.021 J220.U bOuO. 0 5 5 ♦U.0 590V.0c2 blo-J.U GOcu.O 5420.0 5900.023 bl4j,o 59o0.0 bjuo.O S90o.0c4 J1 o o • o -594 0.0 5220.0 590 0.0cb buo(), j 5900.0 5140,0 59uo,0CO 6020.0 btiuu.0 bOuO.O 5 Quo • 0c t •♦900.0 SbcO,0 49u0.0 SQ2O.02b 4900.0 JOCU.0 4900.0 5820.J29 bU2U.O bboO,0 5020.0 5boo. o30 4900,0 5340.0 49O0.0 5340. 031 49^0,0 5100.0 4940.0 5100.0V4. 4900,0 4900,0 4900.0 4980,0«5o 48O0.0 4660.0 4900,0 4900.0

SECTOR 3 LiCTPIT UOTULT

SECTOR 4 'to TP IT nOTULT

SECTOR 5 90TPIT PCTUET

6, HE I Oh T or «<ALl -

HLlGliTa Fu k a h 1C»< PKOb, OR FAILURE IS INPUT TEu( IN FT.)

.uO «iOu,OQ 400.(JO 600.00 BOO,00 1000.00 1200.00 1400.00 1600.00 1 <300.00co04

84

7, HKObMLuLl•1 FAILUKt-

WvuKliv bLUPc = tttii»i.CTOr< PiXOdAblLH Y OF FAlLURLb VALL HEIGHTS 1 THROUGH 10

1 ,00U ,020 .040 ,OoO ,090 ,100 .105 ,110 .120 ,1^02 ,000 ,020 .040 .060 ,090 .100 .lob ,110 ,120 .140

WUhtKiiiG SuUHti = 3b

SttlOK PROBABILITY OF FAILURES WALL HEIGHTS 1 THROUGH 10

1 .000 ,100 ,ISO ,200 ,250 ,300 ,350 ,400 .450 .5002 .000 .100 .150 ,200 ,260 ,300 .350 ,400 .450 ,500

NOTE - LA^T iVoRrxI.NG SLuPu. IS NOT EQUAL TO THE ULTIMATE SLOTE AND HENCE THE PiU/bALiulTY OF FAILURE FOR THE ULTIMATE SLuPE IS INPUTTED SEPARATELY

Ultimaie slope angle =45SlCTUR PROtiAbiLIIY OF FAILURES FOR WALL HEIGHTS 1 THROUGH 10

1 .000 ,100 .200 ,300 ,350 .400 .450 .500 .600 .6502 .000 .100 .200 .300 ,360 .400 ,450 ,500 ,600 ,65u

d. TYPES UF PAILUKl -

SECTOix 1

t i m e i y p l s o f f a i l u r e f o r e a c h y e a r o f l i f e

1 0 u 0 0 0 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 3 2 3 1 2 3 1 2 3 1 2 3 1

SECTOR 2

TIME ITPES OF FAIl URl. FOR cACH YEAR OF LIFE

1 ‘ 0 0 0 0 0 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1

9• TKl NU u ATm f o r m i n i n g c o s t -

Yl AR TREND

10 .0220 . 0 333 . 04

85

biMUuAl lON i iUi bLH id 1. bLiJLH i «-

r.'CHK I i»G SlOi’L /\(«uLL = 26r l/\H STK.CObT bLiit.FI T OTHER BENEFIT

i 0. 0. 0.& 0. 0. 0.$ 0. 0. 0.4 0. 0. 0.b 0. 0. 0.V obAuObb, 0. 0.7 b? 10c>6b. 0. 0.b ooboObb, 0. 0.V 144 30742. 0. 0,10 14719367. 0. U,11 13160937. 0. 0.12 7949330, 0. 0.1 j tilo/610. 0. 0.14 0433444, 0. 0.l b 060644 7 , 0. 0.l b 094 704o. 0. 0.17 9210461, 0. 0.16 949191b. 0. 0.19 0063314, 0, 0,20 0923214. 0. 0.21 9200142, 0. 0,22 9bbl34o, 0. 0.2j 6490047, 0. 0.24 o74964ti. 0. 0.2 b 7019634, 0. 0.26 7300420. 0. 0.27 769243o. 0. 0,2b 7696134, 0. 0.29 2703322, 0. 0.30 261146b, 0. 0.31 292391b, 0. 0.32 bU4U070. 0. 0.33 3 1 6 2 6 0 b , o. 0 .

TOTAL BENEFIT

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86

hOrtKING SLOPE ANGLE = J5

YLAK

1a64bb7b9AU

111c14lb161/1619cO212ccb242b2u27cti296041.4244

bTR.COSr0 .c.0 ,u.0 .

0 1 5 6 2 6 1 ,o 2 » 1 6 9 u .O 4 0 / U 2 4 ,

1 1 2 1 b l 9 o , 1 x 4 6 9 5 0 0 . 1 1 7 6 2 6 6 5 ,

O 4 4 9 9 9 0 . 6b464 9 0 , 0 6 4 2 7 9 4 . 7 0 4 6 0 7 6 . 7 2 5 9 5 2 0 . 7 4 7 7 3 0 b , 7 7 0 1 6 2 b ,

1 0 b 7 o 6 9 o , 1 0 6 9 4 2 0 4 . 1 1 3 2 9 9 7 2 . 1 1 7 6 6 1 7 1 .

o 4 9 0 0 4 7 , 0/49640, 7 0 1 9 6 4 4 , 7 6 0 0 4 2 0 . 75524 60 , 7 o 9 o l 4 4 , 7 2 9 4 6 7 0 , 7 b b b o 2 4 , 7 6 6 9 0 4 9 , 6 2 0 4 6 1 1 . 6 5 4 c 7 9 U .

UcNcFIT

0.0.0.0 .0 .

2 6 8 1 o 3 3 ,2429470.2 4 7 0 0 5 9 .6 2 1 5 5 4 6 .5 2 7 9 6 5 6 .6 5 7 6 2 5 2 .149954Q.15 .44320,1 5 9 0 6 4 9 .1 6 3 6 3 6 9 .1 6 6 7 5 2 0 .1756146,1 7 9 0 2 9 0 ,

- 1 9 1 3 5 6 3 .- 1 9 7 0 9 9 1 .- 2 0 4 9 6 3 0 .-2141o 24.

0 .0 .0 .0 .0 .0 .

- 4 5 9 0 5 4 7 , - 4 7 7 4 1 6 9 . - 4 9 6 5 1 4 6 . - 5 1 6 6 7 4 1 , - 5 3 7 0 2 9 1 .

OTHER BENEFIT

0.0.0,0.0,0.0,0.0.0.0.0.0.0.

. 0 . 0. 0. 0. 0. o. 0. 0, 0. 0. 0. 0. 0, 0, 0. 0, 0.

. 0. 0.

TOTAL BENEFlI

0.0.0.0.0.

2661833.2429470.2476059.3215540,3279856,3378252.1499340,1544320.1590649.163ti3o9.1o 67523.1756146.1790290.

-1913563.-1970991,-2049830.-2161824.

0.0.0.0.0.0.

-4590547.-4774169.-4965136,-5164741.-5570291.

87

a, c o s r -

aOKKIUO SlOPL Ar.GuL z 2b

Yt./\K FAlL.CvST 01 HER CQb'f TOTAL COST INC. COST

1 0 . 0 . 0 .2 o . 0 . 0 .J 0 . 0 . 0 .4 u. 0 . 0 .b 0 . 0 . 0 .6 0 . 0 . 0 .I 0 . 0 . o .d 5 3 5 6 4 . 0 . 5 3 b o 4 ,V V. 0 . 0 .

10 0 . 0 . 0 .IJL 0 . c . 0 .12 0 . 0 . O'.l b 0 . 0 . 0 .14 0 . 0 . 0 .l b 0 . 0 . 0 .1c 0 . 0 . 0 .17 6 1 6 7 6 o . 0 . 6 1 6 7 6 8 ,i t i 0 . 0 . 0 .19 o . 0 . 0 .*U 1 1 0 6 4 1 4 3 . 0 . 1 1 0 6 4 1 4 3 ,< l 0 . 0 . o.C-C 0 . 0 . o .2b 2 6 1 6 2 5 9 . 0 . 2 6 1 6 2 5 9 .24 u . 0 . o .2b 0 . 0 . o .26 4 3 1 6 4 9 7 . 0 . 4 3 1 8 4 9 7 ,27 V. 0 . 0 .2d 0 . 0 . o .29 6 3 9 * 1 4 4 . 0 . 6 3 9 4 1 4 4 .30 U. 0 . 0 .31 2 6 9 . 0 . 2 6 9 .32 2 0 7 4 4 6 6 7 . 0 . 2 0 7 4 4 6 6 7 ,3b o . 0 . o .

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tGHKlWb SLOPc ANGLE = 35rt-Ai< FAIL ,COST ult iEK COST TOTAL COST

i 0 . 0 . 0 .2 u . 0 . 0 .3 0 . 0 . 0 .4 0 . 0 . 0 .b u. 0 . 0 .6 u. 0 . 0 .7 0 . 0 . 0 .6 0 . 0 . 0 .9 0 . 0 . 0 .

10 0 . 0 . 0 .11 0 . 0 . 0 .I'd 0 . 0 . 0 .13 Ct>4, 0 . 2 0 4 ,14 5 4 4 9 7 2 2 . 0 . 5 4 4 9 7 2 2 ,15 0 . 0 . 0 .l b 0 . 0 . o .17 0 . 0 . o .l o 0 . 0 . o .19 1 7 0 . 0 . 1 7 0 .20 5 6 9 / 0 1 4 . 0 . 5 6 9 7 0 1 4 ,21 0 . 0 . o .22 0 . 0 . 0 .23 5 3 9 0 1 2 . 0 . 5 3 9 0 1 2 .24 0 . 0 . o .2 5 0 . 0 . o .26 3 6 9 1 6 5 9 , 0 . 3 0 9 1 6 5 9 .27 0 . 0 . ‘ o .2d 4 7 6 . 0 . 4 7 0 .29 7 0 9 3 0 5 1 , 0 . 7 0 9 3 0 5 1 ,oU 0 . 0 . o.31 5 3 0 , 0 . 5 3 6 .32 o . 0 . o .33 0 . 0 . 0 .

IN C. COST

0.0 .0 .0 .0.0 .0 .-53B3'4. 0 . 0 . 0 , 0 .

284. 5449722.0 .0 .

_ 6J, t i7o8« 0 .

1 7 0 . - 5 1 0 5 5 2 9 .*0,0.-2076446,

0 .0.—626039. 0. 4 7a .

- 1 3 0 1 0 9 2 .0.269.

■20 74 4 06 7 .0.

Incremental NPV of 35° Working Slope Compared to 25°. - Final results.

i 30jvOol, 31 36 -4.-14c 32 /l‘+< j 1. V

bui'Hf.11 , 33 L f.. V.147,09. 64 ^louoi£

5 4t32'.'{ib, 63 036141?o 43V,!otr>, 30 O-ri + ;iu37 0Ow^341, 3/ t> 27. 77c 3o04oi4, 3o 6..1 " -t

4V'll 1h 1 , 69 44 < 36.Liv tbU-'lVBO. Oti ■»34d ^ /* ▲ tvvJul#. Ol 6390:92*6. 02 4 6 3 4 0 6 3

U0«8iL,l, o3 4c-.lt 1714 til C c«» 7 c , 04 oVboc10iv aOolt 60, 03 63 J"" 4t6*o ic761i%, 4 uc c-76it -.017211. 0 / 33L;2Cc 3io b4v<v>ul, •* / *4 *w 1

2642311, 034 7o*.4o?, 7u 4 / V 9 0 14397.75, Jj. 43330064667462. 7i 3763144

^ j 3402627, 7 j 3U6c 4 o Ob'.21u4'J, 74 42771474 o 269 u 6 , 73 404697 7:4it:t313L, 7o 430 3 9 0

c! 6726264,. 77 44-2oi 4io 336916/, 7o oO:7bv0c'j 3364262. 79 3337946

4666334, oO 4 7o29o 7w i c+26129. fai 479114bit. b oo1620, 62 2ull496io tilclol4, 03 300046?ej1. 3303447, 4266310b V 3920073. 03 4bjno7D

co-oGobG, OO 0 0 192.0o / u497o?6, o7 4 9226c4-0 379717,.. 4 449 / 7 b

4ilC3o7, oV 320211.4*.0 4674/91. 90 6794o66

3721261, 91 3^766994i 3027413, 9t 4c4l3‘*3•»0 4343eK>. 96 6964 lv-74‘« 2'i70co9, 94 43189CG40 4749263, 95 6 v 4 v v c 44(. 4176707. bob:joJt '7 476794 0, 97 3 / 31c.. 1••U V t 77303, 90 3376267

4702022. 99 6936067oo 4640436, lOu 4v33ci4

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90

Run No. 1. Clean up Cost Equal to 1.25 Times the Unit Mining Cost

WORKlWv AVERmGc inPV u F IN C . G c i lE F lT AND IN C . COST FOR STAn OARDbLOPt lOCSiF .vUAl lOiiS AND AT OISCOUNI RATE OF . 1 5 0 D E V IA T IO N

kb 0. 0 .^ 5 4 7 2 3 7 7 6 . 1 0 4 4 3 0 3 .

Run No. 2. Clean up Cost Equal to 3.0 Times the Unit Mining Cost

•aUKKINv AVLRa Gu i.PV OF IN C . G uNuFlT AND IN C . COST FOR STANDARDSLCHl. I u OSIN j LA T IO n S AND ulSCOUNl R,i. FE OF . 1 5 0 D E V l^ l ION

2535

0.3 1 3 3 2 2 0 .

0.2 5 0 6 3 1 3 .

91

Run No. 3 Clean up Cost Equal to 1.25 Times the UnitMining Cost and 2 5% Increased Probability of Failure

1,'up.ix ll.ljSLCPu<:5JS

AWiKAw: NrV OF INC. p^f^FlT At.:) INC. CO<T FOR lUt^I.iULAI A Mi-1 AT . 1SC0UNT P. Alt' OF . ISO

n.442)816.

STAxL'ARU u L V I a T I O i

C.1 0 7 2 5 6 9 .

Run No. 4 Clean up Cost Equal to 3.0 Times the Unit Mining Cost and 25% Increased Probability of Failure

Avr.rUNu AVCK k V v Z.Pv Jf I„v. cc. Ji£r IT 6K0 iwC, COS! FO k STAu LARO5 w U r >c. 1 J v ^ * N ‘..L.’;T i O u j Ainu AI O l S C O U i i l F A % L Op .150 D E V I A T I O N

0. 0,^ 2 4 1 5 5 2 6 . 2 5 7 4 2 0 0 .

APPENDIX D

FINANCIAL RISK ANALYSIS COMPUTER PROGRAM

92

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PROGRAM INRISK(INPUT,OUTPUT,T APR1=INPU T ,TA nr3 = 0 U T P U T ,T APF4 , TAP F A )

T H I S P R O G R A M R F A O S IN A L L T H E I N P U T D A T A A N O P E R F O R M S THE F I N A N C I A L A N A L Y S I S SY C A L L I N G D I F F E R E N T R O U T I N E S .R A J A P. U P A O M Y A Y , OEP T . OF M I N . A N D G E O L . E N G . , U. OF A

D I M E N S I O N P V I N ( I C G ) , R O I I N ( 1 3 0 ,WG I N<(100) , W E L ( 1 0 0 , 3 ) , W G R O N C ICO, H , 1 0 C F R ( 1 3 0 , 3 ) , O C F R O I (1DC, 3)C O M M O N N A M E (20 » . N U L S L , N S I M , N S L O P , R R A T E , F E D R , P M T R , P I T R , O E P L R , N D A Y , l C A P A C , C O N S , C O N O . N E X P , N O C , N M M L , S V A R ( 1 7 , 1 4 > , 0 N A S T ,C C A P , G R A C ( 3 , 6 0 ) , 2 A C O S T (60) ,X CCS T ( 3 , 6 0 ) , T C T ( 3 , 6 0 ) , N N ,N P R O O ,C F (63),3 N W R S L ( 3 ) , P N V ( 1 3 C » 3 ) , P V I N C (10 0 , 3 ) , 3 E N O T (3, 60) . S C O S T (3,60) C O M M O N / R U N / N T A X , N O U G . N P L O T D A T A N T A P E / 4/R E A D 1 0 , N A M E10 F O R M A T ( 2 C A 4 )N O U T = 0 D T T O N TO P R I N T I N P U T D A T A , 1 = Y E SNT AX = O P T I O N F O R U S E R S U P P L I E D R O U T I N E TO C O M P U T E D E P R E C I A T I O N , D E P L E T I O N , A N D T A X E S A C C O R D I N G TO T H E A M E R I C A N T A X L A W .

= 1 YESN B U G = O P T I O N TO P R I N T I N T E R M E D I A T E R E S U L T S , 1 M E A N S YES .R E A D 1 1 , N O U T , N T A X , N B U G

11 F O R M A T (3110)R E A D IN T H E F I X E D V A R I A B L E S .N U L S L = U L T I M A T E S L O P E A N G L EN S I M = N U M B E R O F S I M U L A T I O N S F O P E A C H W O R K I N G S L C P E N S L O P = N U M B E R OF W O R K I N G S L O P E S T O BE T E S T E D N D A Y = N U M B E R OF W O R K I N G D A Y S 3 EP Y E A R N N = P R E - P R O D U C T I O N P E R I O D IN Y E A R SN E X P = N U M B E R OF Y E A R S R E Q U I R E D F O R E X P L O R A T I O N S T A R T I N G F R O M T H E F I R S T Y E A R .N O C = N U M B E R OF Y E A R S R E Q U I R E D F O R W A T E R A N D L A N D A Q U I S I T I C N A N D O T H E R L E G A L E X P E N S E S .N M M L = N U M B E R OF Y E A R S P E U U I P E O F O R M I N E A N D P L A N T C O N S T R U C T I O N . N P R O D = P R O D U C T I O N L I F E 0 F T H E M I N E .R R A T E = R E Q U I R E D R A T E OF R E T U R N .F E D R = F E D E R A L I N C O M E T A X R A T E .P M T R = P R O V I N C I A L M I N I N G T A X R A T E .P I T R = ° R O V I N C I A L I N C O M E T A X R A T E .O E P L R = D E P L E T I O N RATE.C O N S = P E R C E N T A G E CF C O P P E R IN T H E C O N C E N T R A T E .C O N O = P E R C E N T A G E OF C O R P E R IN THE C E M E N T C O P P E R .O W A S T = P E R C E N T A G E OF O X I D E O R E IN T H E W A S T E .O C A P = C A P A C I T Y OF THE L E A C H I N G P L A N T P E R D A Y .C A P A C = D A I L Y P R O D U C T I O N ( M I L L C A P A C I T Y ) .R E A D f i , N U L S L , N S I M , N S L O P , N D A Y , N N , N E X P , N O C , N M M L , N P R O O8 F O R M A T ( B I G )R E A D 9 , R R A T F , F E D R , P M T R , P I T R , O E P L R , C O N S ,C O N O , O W A S T , O C A P , C A P A C

9 F O R M A T ( S F 5 . 3 , 2 F 1 5 . 0 )ND = NN + N P R O DC

94C Pf AO IN I M F S T O C H A S T I C V A R I A B L E S T H A T A R E N O T D E P E N D E N T ON THEC W O R K I N G S L O ° E A N G L E .C R E A D 16. ( < S V A » ( N , K >.'<=1.131 tN= 1 , 1 7 >16 F O R M A T ( F 5 . P . 3 F 1 C . 3 . P F 5 , .31CC R E A D IN THE S U L P H I D E O R E G R A D E F O R E A C H Y E A R A N D E A C H W O R K I N GC S L O » E A N G L E .CC G R A D (I ,KK > = G R A D E OF THE S U L P H I D E ORE F O R I TH W O R K I N G S L O P E A N DC K K TH Y E A R .C

R E A D 1 9 , ( N W R S L ( T ) t I = l . N S L O P l19 F O R M A T (31 101D O 31 I = 1 , NSL O pR E A D 1 7 , ( G P A O < I , K K ) , K K = l , N D )

17 F O R M A T ( 1 6 F 5 . 3)31 C O N T I N U ECC C H E C K FOR THE I N P U T D A T A P R I N T O U T O P T I O N , IF ON C A L L S U B R O U T I N EC I N O U T TO P R I N T THE I N P U T D A T A .C I F ( N O U T . G T . 0) 4 , 54 C A L L I N O U TC 5 NO = N E X P f 1

N N O = N E X P «- N O C N C O N = NN - N M M L N C C N = N C O N + 1

CC I N I L I Z E T H E A R R A Y V A R I A B L E S .C .D O 21 IS = l . N S I M

P V I N ( I S ) = 0.0 R O I I N d S l = 0.0 W G I N ( I S ) = 0.0 D O 21 I = 1 , N S L O P P N V (I S ♦I ) = 0.0d c f r ( i s , i i = c . cW £ L ( I S , I ) = 0.0 P V I N C ( I S , I ) = 0.0 D C F R O I ( I S , I ) = 0.0 W G R O W ( I S , 11 = 0.0 21 C O N T I N U E

C P R I N T 3 , N A M E3 F O R M A T ( 1 H 1 , 4 C X , * - - I N T E R M E D I A T E R E 3 U L T S - - * / / 5 X , 2 0 A 4 / / / 1

CC S I M U L A T E AS M A N Y T I M E S AS R E Q U I R E D .C DO 15 IS = l . N S I MCC G E N E R A T E O N E V A L U E F O R E A C H S T O C H A S T I C V A R I A B L E S ( 1 T H R O 14)C BY C A L L I N G THE S U B R O U T I N E G E N E R .C DO 45 N = 1 , 1 4 45 S V A R ( N , 14) = C.C

D O 20 N = 1 , 1 4 C A L L G E N E R (N)

20 C O N T I N U E

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IF (NOUG. r,T. G1 2 2 , 2 322 P & I W T 6 , IS6 F O ^ M A T ( / / 4 0 X , ' S I M U L A T I O N NO. = * , I3Z)Pf AO IN T H F D A T A G E N E R A T E D fTY THE B E N E F I T C O S T M O D E L F R O M T H E M A G N E T I C TAPE.NT A P E = U N I T N O . A S S I G N E D TO T H I S T A P E .

23 00 30 T = l . N S L O P T O V 2 = 0.0 C L A I M = 0 . 0T U V 3 = 0.0 O I N V = 0.0 O O 42 K K = 1 , NO 42 C F (K<) = 0.0OO 40 KK = 1 , N DA C O S T ( K K ) = A V E R A G E U N I T M I N I N G C O S T IN KK TH Y E A R .X C O S T ( I . K K t = P P E- S T R I P P I N G OR S T R I P P I N G C O S T S F O R I T H W O R K I N G S L O P E A N D KK TH Y E A R .T C T (I ,KK) = C O S T OF F A I L U R E F O R I T H W O R K I N G S L O P E AND KK TH Y E A R . C F ( K K ) = C A S H F L O W IN K K TH Y E A R .

R E A D ( N T A P E , 25) A C O S T ( K K ) , X C O S T (I , K K ) , B E N O T (I , K K ) , T C T (I , KK)25 F O R M A T ( F 5 . 3 , 3 F 1 0 . 0)S C O S T (I , KK) = X C O S K I, KK) - 8 E N 0 T (I, K K )G E N E R A T E O N E V A L U E F O R E A C H Y E A R F R O M THF S T O C H A S T I C V A R I A B L E S ( 15 T H R U 17) BY C A L L I N G T H E S U B R O U T I N E G E N E R .0 0 18 N = 1 , 3 N L - N + 1 4 18 S V A R ( N L , 1 4 ) = 0.0 0 0 50 N = 1,3 NL = N ♦ 14 C A L L G E N E R (NL)

50 C O N T I N U EC A L L S U B R O U T I N E CASHF|_ TO C O M P U T E T H E C A S H F L O W S .C A L L C A S H F L ( I S » I , K K , N N O , C L A I M , T D V 2 , T O V 3 , 0 1 N V )

40 C O N T I N U EI F ( N B U G . G T . 0) 3 2 , 3 332 P R I N T 1 0 1 , N W R S L ( I ) , N O101 F O R M A T (/1 O X , ' W O R K I N G S L O P E A N G L E = ♦ , I 3 / / 1 0 X ,* C A S H F L O W S F O R Y E A R S 1 1 T H R O U G H ' ,13/)

P R I N T 1 0 2 , ( C F C K K ) , K K = 1 , N O )1 02 F O R M A T ( 5 X , 1 0 F 1 2 . 0)

C O M P U T E THE N E T P R E S E N T V A L U E , O C F R O I , A N D W E A L T H G R O W T H R A T E .33 C A L L N E T P R V (PV,NO)

P N V (I S ,I ) = pV

C A L L S U B R O U T I N E O C F R O I TO C O M P U T E O C F R O I .C A L L O C F R O I ( I S , R O D O C F R ( I S , I ) = R O I

C

O O

O O

O O

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96

C A L L S U B R O U T I N E W E L G R TO C O M P U T E T H E W E A L T H G R O W T H R A T E .C A L L W E L G R ( W G R )WEL(IStI> = WGR 30 C O N T I N U EC O M P U T E THE I N C R E M E N T A L N E T P R E S E N T V A L U E .0 0 61 I = 1 ♦ N S L O F I F ( I . G T . l ) GO T O 62 PV INC (IS, I) = 0.C n C F R O I ( I 5 , I ) = C.J W G R O W ( T S , I * = 0.0 GO TO 61

62 PV INC (IS, I) = R N V d S . I ) - P N V ( I S , 1 )O C E R C I (I S , I > = O C F R ( I S , I ) - O C R R d S . l )WGR0 W( I S , I ) = WE L ( I S , I > - W F l ( I S , l >61 C O N T I N U E

15 C O N T I N U E M T T = N S I MS O R T THE V A L U E S IN A S S E N O I N G O R D E R BY C A L L I N G S U B R O U T I N E S O R T .I F ( N O U G . G T . 0) 4 3 , 4 4

43 P R I N T 4646 F O R M A T ( 1 H 1 , 2 0 X , ♦ S O R T E D V A L U E S * / / )44 D O 86 I = 2 , N S L O P

D O 65 IS = l . N S I M P V I N ( I S ) = P V T N C ( I S , I )R O I I N d S ) = O C T R O I (IS,I)W G I N ( I S ) = W G R O W ( I S , I )85 C O N T I N U EC A L L S O R T ( N S I M , N S I M , P V I N )C A L L S O R T ( N S I M , N S I M , R O I I N )C A L L S O R T ( N S I M , N S I M , W G I N )I F ( N B U G . G T . 0) 4 7 , 4 8

47 P R I N T 5 8 , N W R S L ( I )58 F O R M A T ( / / 5 X , * W O R K I N G S L O P E = * I 3 / / 5 X ,* S I M U L A 11 O N * 1 0 X , ♦ N P V * 1 0 X , * D C F 1 R O I * , 1 0 X , * W G R * / )

D O 59 IS = 1 , N S I MP R I N T 5 7 , I S , P V I N ( I S ) , R O I I N d S ) . W G I N (IS)

57 F O R M A T ( 1 1 1 , F 1 8 . 0 . 2 F 1 2 . 3)59 C O N T I N U E48 P R I N T 7 0 , N W R S L ( I )70 F O R M A T ( / / 1 H 1 , 3 0 X , * - - F I N A L R E S U L T S • - - * / / / 1 0 X , * W O R K I N G S L O P E A N G L E * 1 , 1 3 / / / )MT = 1

C A L L P R O O I S ( P V I N , M T , M T T )HT = 2C A L L P R O D I S ( R O I I N , M T , M T T )MT = 3C A L L P R O O I S ( W G I N , M T , M T T )86 C O N T I N U E S T O P E N D

S U B R O U T I N E I N O U TC

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T H I S S U B R O U T I N E P R I N T S OUT ALL I N P U T D A T A P E A O I N F R O M T H E C A P O S .C O M M O N N A M E (20 > * N U L S L , N S I M , N S L O P ,R R A T £ ,F E O R i P M T R ,P I T R , 0 E P L R ,NO A Y ,

1 C A P A C , C 0 N S , C G N 0 , N E X P , N 0 C , N M M L » S V A R ( 1 7 , 1 4 ) ,O W A S T , C C A P , G R A n ( 3 , 6 0 ) , 2 A C O S T ( o O > , X C O S T ( 3 , 6 0 ) » T C T ( 3 , 6 0 ) ,N N , N P R O O ,C F (60» ,3 N N R S L (3) , P N V ( 1 0 G , 3 ) , P V I N C (10 0 , 3 ) , OE.NOT ( 3, 60 ) , S C O S T ( 3 , 6 0 )P R I N T 11C11C F O R M A T ( / / 1 H 1 , 4 3 X , * — I N ^ U T D A T A - - * / / )P R I N T 1 2 0 , NAM E 120 F O R M A T ( 5 X , * P R O ^ E R T Y - * 2 0 A 4 / X )P R I N T 130130 F O R M A T ( 2 X ,* 1• f I X E O V A O I A R L E S - * / / / )P R I N T 1 4 0 , N U L S L , N S I M , N S L O P , N D A Y , N N , N E X F , N O C , N H M L , N F R O O 140 F O R M A T ( 5 X , ^ U L T I M A T E * , H X , » N U M B E D O F * % X , * N U M j E R O F * 8 X , * N U M O E R OF * ,

1 / 5 X , * S L O P E A N G L E * 5 X , * S I M U L A T 1 0 N S * 6 X , * W 0 R K . S L 0 P E * 6 X , * W O R K . D A Y S / Y R * 2 / Z I 1 2 , 1 1 6 , 1 1 5 , I 1 8 Z Z / 5 X , * P R F - P P 0 0 . * f l X , * E X P L O R A T I O N * X X , * Y R . F O R W A T E R 3 * 8 X , * Y R . F 0 p M I N E A N O * A Y , * P O Q O . * Z 5 X , * p E R I O 0 * 1 1 X ,* P E p I O O * 1 3 X ,* AND LA 4 N O A 0 , * 6 X , * p L A N T C O N S . * 1 2 X ,* Y E A R * Z Z 1 1 0 , 1 1 7 , 1 1 8 , I 1 9 , 1 2 2 Z Z Z )P R I N T 1 9 0 , P R A T E , F E O R , D M T R , P I T R ,O F P L R ,C O N S ,C O N O ,O N A S T ,O C A p , C A P A C 150 F O R M A T ( 5 X , * R A T E 0 F * 4 X , * F E D . I N C 0 M E * 4 X , * PRO V . M I N I N G * 4 X , * P R O V . I N C O M E * 1 4 X , * O E pLE T I O N * 4 X , * C O N C . G P A 0 E * Z 5 X , * P F T U R N * 6 X , * T A X P A T £ * 6 X ,

2* T AX R A T E * 7 X , * T AX R A T E * 7 X , * R A T E * P X , * ( S U L P H I O E ) * Z Z F 9 . 3 , F 1 1 . 3 , •3 4 F 1 5 . 3 Z Z Z 5 X , * C E M . C 0 p P E R * 4 X , * O X I O E O R E I N * 4 X , * C A p A C I T Y OF THE *,4 7 X , * M I L L * Z 7 X , * G R A D E * 8 X , * THE W A S T E * 6 X , * L E A C H . P L A N T Z 0 A Y * 4 X , 5 * C A P A C I T Y Z 0 A v * / X F 9 . 3 , F 1 7 . 3 , 2 F 1 8 . C Z Z )P R I N T 5

5 F O R M A T ( Z 2 X , *2. S T O C H A S T I C V A R I A B L E S - * Z Z Z I DO 10 N = 1,17G O TO ( 1 1 , 1 2 , 1 3 , 1 4 , 1 5 , 1 6 , 1 7 , I S , 1 9 , 2 8 , 2 1 , 2 2 , 2 3 , 2 4 , 2 5 , 2 6 , 2 7 1 N

11 P R I N T 3131 F O R M A T ( 5 X , * E X P L O R A T I O N C O S T ( $ ) *Z1

G O TO 2012 P R I N T 3232 F O R M A T ( 7 5 X , * R O Y A L T Y ( P E R C E N T A G E ) * Z )

G O TO 2013 P R I N T 3333 F Q P M A T ( Z 5 X , * 0 R E G R A D E - O X I O E * Z )G O TO 2014 P R I N T 3434 F O R M A T ( Z 5 X , * R E C O V E R Y - S U L P H I D E O R E * Z )

G O TO 2015 P R I N T 3535 F O R M A T ( 7 5 X , * R E C O V £ R Y - O X I D E O R E * Z )

G O TO 2 016 P R I N T 3636 F O R M A T ( Z 5 X , * C A P I T A L E X P E N D I T U R E - M I N E ( ? ) * Z )G O TO 2017 P R I N T 3737 F O R M A T ( Z 5 X , * C A p I T A L E X P E N O I T U P E - M I L L ( T ) *7)G O TO 2018 P R I N T 3838 F O R M A T (Z 5 X , * C A p I T A L E X P E N D I T U R E - L E A C H I N G P L A N T ( S)* Z)G O TO 2019 P R I N T 3939 F O R M A T ( Z 5 X , * W A T E R ♦ L A N D A Q U I S I T I O N C O S T ($> *71 G O TO 2 028 P R I N T 4 040 F O R M A T ( 7 5 X , * P O S T C O N C . C O S T ( $ 7 T O N C O N C . ) * Z )G O TO 2021 P R I N T 52

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52 r o R M A T ( / 5 X « " P O S T L C A C H . C O S T ( % / T O N CE M . C O P P E R ) * / )G O TO 2022 P R I N T 51

53 F O R M A T ( / 5 X , ' M I S C E L L A N E O U S C O S T (•’‘/ T O N O R E ) * / )G O TO 2323 P R I N T 54

54 F O R M A T (/ 5 X , ' S A L V A G E V A L U E (%) */)G O TO 2024 P R I N T 5555 F O R M A T ( / 5 X , ' W O R K I N G C A P I T A L (%)*/)

G O TO 2025 P R I N T 5656 F O R M A T (/ 5 X , ' P R I C E OF C O P P E R ( % / T O N C U ) */)G O TO 2026 P R I N T 5757 F Q P M A T ( / 5 X , ' M I L L I N G C O S T ( % / T O N O R E ) * / )

G O TO 2027 P R I N T 5858 F O R M A T ( / 5 X , ' L E A C H I N G C O S T ( % / T O N O R E ) * / )20 M = S V A R (N * 1)G O TO ( 4 1 , 4 2 , 4 3 , 4 4 , 4 5 ) M41 P R I N T 5 1 , S V A R ( N , 2 ) , S V A » ( N , 3 )51 F O R M A T ( 1 G X , * N 0 R M A L * / / 5 X , * M E A N * 2 0 X , * S T D . O E V . * / F 1 3 . 3 , F 1 5 . 3 / )

G O TO 1342 P R I N T 6 1 , S V A R ( N , 2 ) , S V A R ( N , 3 ) , S V A P ( N , 4 )61 F O R M A T (1 0 X , * T R I A N G U L A R * / / 5 X , ' M I N T M U M * , 1 5 X , * M O S T L I K E L Y * 1 5 X ,1 * M A X I M U M * / F 1 5 # 3 , F 2 5 . 3 , F 2 5 . 3 / )G O TO 1043 P R I N T 7 1 , S V A R ( N , 2 ) , S V A R ( N , 3)

71 F O R M A T ( 1 C X , * R E C T A N G U L A R * / / 5 X , * M I M I M U M * 1 5 X , * MA XI M U M * / F 1 5 . 3 , F 2 5 . l/> G O TO 1044 P R I N T 8 1 , S V A O ( N , 2 ) , S V A P ( N , 3 ) , ( S V A R ( N , J ) , J = 5 , 1 3 )81 F O R M A T (1C X , ' H I S T O G R A M * / / 5 X , ' O F G . L I M I T * 1 5 X , ' I N T E R V A L * 1 5 X ,

1 ' P P O B A B I L I T I E S OF E A C H CL A S S * / F 1 5 . 3 , F 2 5 . 3 , 5 X , 9 ^ 6 . 3/)G O TO 10

45 P R I N T 9 1 , S V A R ( N , 2191 F O R M A T (IQ X , ' C O N S T A N T * / / 5 X , * V A L U E = * F 1 2 . 3 / I 10 C O N T I N U E

P R I N T 20 0 , ( N W R S L (I ),1 = 1,3)200 F O R M A T ( / / 5 X , * W O R K I N G S L O P E A N G L E T O BE T E S T E D = * 1 2 * , * 1 2 * , * 1 2 * O E G 1* / /)P R I N T 201

201 F O R M A T ( / 2 X , *3. O R E G R A D E - S U L P H I D E * / )P R I N T 2 u 2 , N P R O O2 0 2 F O R M A T ( / / 5 X ,' W O R K . SLOt>E *25 X, ' O R E G R A D E F O R P R O D U C T I O N Y E A R S * , / 1 8 X , * A N G L E * 3 2 X , *1 T H R O U G H * , I D

DO 2 0 3 I = 1,N S L O P2 0 3 P R I N T 2 0 4 , N W R S L ( I ) , ( G R A O ( I , K K ) , K K = 1 , N P R O O )234 F O R M A T ( / I 1 1 , 5 X , 1 6 F 6 . 3 , 2 ( / 1 6 V , 1 6 F 6 . 3))

R E T U R NE N D

S U B R O U T I N E CASHFL(I S ,I , KK, N N O , C L A I M ,T O V 2 , T O V 3 , O I K V )T H I S S U B R O U T I N E C O M P U T E S C A S H F L O W S F O R E A C H P R E P R O D U C T I O N A N D P R O D U C T I O N Y E A P S .

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COMMON NAME (20),NUL S L «NSI H , N C L O P , R R A T E ,F E D R ,PMT« ,PITR,1FPLR,N0AY, 1CAPAC,CONS,CCNOX.'CXP,HOC,NM'IL.SVAP (17,14) , 0 W AS T , CCA P , GR AD ( 3 , 60 ) , P A C O S T (6 j ) ,X COS T (3,60 1 , T C T (3,G O >,N N ,NPROO,C F (60) ♦3 N W R S L (3),PNV(1J0,7),PVTNC(130,3),8 E N O T (3,63) ,S C O S T (3,60)COMMON/RUN/NTAX,NPUG,N^LOT

COMPUTE CASH FLOWS FOR THE °RE-PRODUCTION Y E A R S .

SUMST = DEVEL O P M E N T (0" P R E - S T R I P P I N G )C O S T S .

TF(KK.OT.NFXP) GO TO 70C F I K K ) = -( (SVAR (1, 14) / NEXP) tSCOST ( I , KK )<-T C T (I , KK) )RETURN

70 IF(KK.GT.NNO) GO TO BOCF(KK) = -( (SVAR (9,14)/NOC) «■ SCOST (I , K K ) <-TCT(I,KK))RETURN

80 IF(KK.GT.NN) GO TO DOCF(KK) = - ( ( (SVAR(6,14)*SVAR(7,14)*S V A R (3,14)>/NMML)*SCOST(I,KK)+TC

I T (I ,KK) )RETURN

COMPUTE THE CASH FLOWS FOR THE PRODUCTION YEARS.

90 SUMST = C.ODO 55 KL = 1,NNSUMST = SUMST 4- XCOST(I.KL)

55 CONTINUEEXOEV = SUMST + S V A ® (1,14)ZCOST = CAPAC*NDAY* (ACOST (KK) 4-SV AR (16, 1 4) «■ SVAR ( 12, 14) ) 4-SCOST ( I, KK

U + T C T (I ,KK)1 + T C T (I,KK)SGROS1 = C A P A C ' N O A Y + G R A D d , KK)*SVAR(4,14)*SVAR(15,14)SGR0S2 = ((CAPAC*NOAY*GPAD(I,KK)I/C O N S )vSV A R (10,14)SGROSS = SGROS1 - SGROS2

OTON = TONNAGE OF THE OXIDE ORE RECOVERED IN ONE YEAR.OCAPAC = YEARLY CAPACITY OF THE LEACHING PLANT.OINV = INVENTORY OF THE OXIDE ORE.OLEACH = OXIDE ORE LEACHED IN THE PARTICULAR YEAR.

OCAPAC = OCAP * NO AYOTON = (XCOST(I,KK)/ACOST(KK))*OWAST IF(OTON.L T.OCAPAC) 71,72

71 IF(0INV.GT.0.0) 73,7473 I F ((OINV4OTON)-OCAPAC) 75,76,7775 OLEACH = OINV f OTON

0 1 NV - 0.0GO TO 81

76 OLEACH = OCAPAC OINV = 0.0GO TO 81

7 7 OLEACH = OCAPACOINV = (OTON+OINV) - OCAPAC GO TO 81

72 IF(OTON.EQ.OCAPAC) 78,7978 OLEACH = OCAPAC

GO TO 8179 OLEACH = OCAPAC

OINV = OTON - OCAPAC GO TO 81

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74 OLEACH = OTON

C O M P U TE THE G? OSS PROFIT F P Q M THE O XIOE OPE.

81 OCOST = OLEACH * SVARt17.14)COST = 7COST 4- OCOST0GR0S1 = OLEACH * SVARCJ.14) * S V A R (5.14) * SVAR (15,14)OGROS ?. = ((OLEACH * SVAR(3, 14) ) /C0N0)'*SVAR (11,14)0 GROSS = 0GR0S1 -0G?0S2

COMPUTE THE TOTAL GROSS PROFIT FROM DOTH OXIOE A NO THE SULPHIDE ORE.

TGROSS = SGROSS + OGROSS

COMPUTE THE ROYALTY AND THE GROSS PROFIT.

ROYAL = TGROSS * SVAR(2,14)TOINC = TGROSS -ROYAL - COST

CHECK IF THIS PROGRAM IS BEING USED FOR PINES IN THE UNITED STATES, IF YES CALL USER SUPPLIED ROUTINE TO COMPUTE DEPRECIATION , DEPLETION AND TAXES.

IF(NTAX.GT.O) GO TO 30

CALL SUBROUTINE OEPRN TO COMPUTE THE ACCELERATED CAPITAL COST ALLOWANCE.

CALL SUBROUTINE OEPRN TO COMPUTE THE ACCELERATED CAPITAL COST ALLOWANCE.CALL SUBROUTINE OEPRN TO COMPUTE THE ACCELERATED CAPITAL COST ALLOWANCE.

IF(TOINC.GT.0.0) 6 4,65 64 CALL DEPRN(T0V2,TOINC,TEDINC,TCDEPP)

I F (TEOINC.GT.C.0) 100,200

DEDUCT CANADIAN EXPLORATION AND DEVELOPMENT EXPENCES.

TEDINC =EXPENCES EXOEV =CLAIM =UNUSE = EXPLORATION AND DEVELOPMENT COST YET TO BE ALE XD =BDEP = P PROF N =TCOEPR =DEPLC =FED = FE PROVM =PROVI =

N EXPL ORA

T BEFORE

AT ION ANDAT ION ANDAT ION ANDAT ION AND

OF EXPLOR ATI ON

NT C O S T S .NT DEDUCTION CLNT COST YET TONT COST DEDUCT 11

IED TO DATE. CLAIMED.FOR THAT YEAR.

ROFIT BEFORE DEPLETION. NET P R O F I T .DEPRECIATION CLAIMED.

DEPLETION CLAIMED.DERAl TAX.PROVINCIAL MINING TAX. PROVINCIAL INCOME TAX.

100 UNUSE = EXOEV - CLAIMIF(UNUSE.LE.0.0) GO TO 200 IF(UNUSF - TEDINC) 110,110

110 ALEXO = UNUSE GO TO 14 C

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130 ALEXO = TEDTNC 140 CLAIM = CLAIM + ALEXO

GO TO 250 200 ALFXO = C.O 250 fU)Ep = TEOINC - ALEXO

IE(HOFP.GT.0.0) 270,240

CALL SUBROUTINE OEPL TO COMPUTE DEPLETION ALLOWANCE AND TAXES.

270 CALL OE^L(OOED . T O V 3,CU^ I NV , E X O E V ,P K O F N ,O E P L C )GO TO 95TCOEPC1 = 0.OEPLC ii

FED = 0.0PROVM — C.OPROVI = C.OPROFN — ij . cCF(KK) = TOGO TO 40OEPLC = C.OFED = 0 .0PRO V M = 0.0PROVI = C.OPROEM = C.OGO TO 95

CALL USER SUPPLIED ROUTINE FOR AMERICAN TAX LAW.

30 CALL USTAX

COMPUTE THE CASH FLOW.

45 CF(KK) = PROFN + TCOEPR + OEPLC » ALEXO 40 RETURN

END

SUBROUTINE GENER CN)

THIS SUBROUTINE GENERATES ONE VALUE FROM THE GIVEN PROBABILITY DISTRIBUTION OF THE STOCHASTIC VARIABLE.

D I M E N S I O N P D O B ( q)COMMON N A M E (201,N U L S L ,NSIM , N S L O P ,R B A T E ,F F O R ,P M T R ,P I TR,O E P L R ,N OAY,

lCAPAC,CONS,CCNO.NEXP,NOC,NMML,S VAR(17,14),OWAST,CCAPtGRAD(3,60>, 2 A C O S T (60) ,XCOST(3»60L, T C T (3,60)«NN . M DR O O « C F (60)»3 N W R S L (3),PNV(10 0,3),PVINC(10 0 , 3 ) , B E N O T (3,601♦SCOST(3,60T M = SVAR(N.l)GO 10(23,30,40,50,60) M

20 AN = SVAP (M,2>PN = SVAP (N ,3)CALL XNORMtAN,QN,VALUE)GO TO 25

30 AT = SVAP(N,21 BT = SVAP(N,3)CT = SVAR (N,4l

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CALL T9IA'JG (AT,nT,CT ,VALUF) GO TO 2G

40 AR = SVAP (N,2) np = S V A R C N , 3)CALL RFCT (AP,BP* VALUE-)GO TO

50 AH = SVAP (N,2)OH - S V A R ( M , 3)00 15 I = 1,9 M = J * 4PROa<I) = SVAR(NtM)

15 CONTINUECALL HISTC(AH,9H,PR09,VALUE) GO TO 25

60 VALUE = SVAR(N,2)25 SVAP(N,1 4 ) = VALUE

RETURN C NO

SUBROUTINE XNORM(AN»BN,VALUE)

THIS SUBROUTINE GENERATES ONE VALUE FROM A NORMAL DISTRIBUTION WITH A MEAN OF AN, AND A STANDARD DEVIATION OF BN.

X = RANF(O)VALUE = AN + SQRT(-2.0*ALOG(Xn*COS<6.2ft31853*Xl*3NRETURNEND

SUBROUTINE TRIANG*AT,8T,CT,VALUE)

THIS SUBROUTINE GENERATES A VALUE FROM A GIVEN TRIANGULAR DISTRIBUTION WITH A MOST LIKELY VALUE OF AT, A LOWER LIMIT OF BT, AND A UPPER LIMIT OF CT.

PML - 2./ (CT-3T)PPML = .5*(AT-DT)*PML SL1 = P M L / (AT-BTi SL2 = PML/(CT-ATI X = R A N R (G)IF(X-PPML) 10,10,12

10 VALUE = BT + SQRT(2.3/SL1*X)GO TO 15

12 PW = X - PPMLVALUE = AT + (PML-SORT(PML*PML-2.0 *SL2 * P W ) )/SL2

15 RETURN END

SUBROUTINE PECKAR,OR, VALUE)

THIS SUOFOUTINE GENERATES A VALUE FROM A GIVEN RECTANGULAR DISTRI­BUTION WITH A LOWER LIMIT OF AP, AND WITH AN UPPER LIMIT OF BR.

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X = P A N F (0)VALUE = RR - X*(BR-AR»RETURNEND

SUBROUTINE HISTO(AH,RH,PROD,VALUE I

THIS SUBROUTINE GENERATES ONE VALUE 'FR01 A GIVEN DISTRIBUTION WITH A BE GENING CLASS LIMIT OF AH,LENGTH BETWEEN CLASS INTERVAL OF RH, AND A PROBABILITY OF I TH CLASS OF PROB(I).

DIMENSION PROB(q),CUPROB(P),C L A S S (9)

DO 10 I = 1,9cupR onm = o.oCLASS(I) = C.O

10 CONTINUEDO 15 I = 1,9 N = ICLASS*I) = AH + N +8H IF(I-l) 16,16,17

16 C U P R 0 9 (I ) = P R O D (I )17 C U P R O B C I ) = CUPROB (1-1) ♦ PROD(I)15 CONTINUE

X = R A N F (0)DO 20 I = 1,9 M = II F {X - C U P ROO(I)) 30,30,20

23 CONTINUE30 IF(M - 1) 31,31,3231 VALUE = AH + X / C U P R O B (M )*BH

GO TO 4032 VALUE = CLASS(M-l) + (X - C U P R O B (M-1 ) ) / (CUPROB(M)-CUPROB (M-l))*BH 40 RETURN

END

SUBROUTINE DEPRN(T0V2,TOINC,TEDINC,TCDE°R)

THIS SUBROUTINE COMPUTES THE ACCELERATED CAPITAL COST ALLOWANCE FOR THE CANADIAN TAX LAW.

C O M M O N N A M E (20) ,N U L S L , NSI M , N S L O P , R R A T E , F E D R , P M T R ,P IT R , D E P L R ,NO A Y , 1 C A P A C , C 0 N S , C 0 N 0 , N F . X P , N 0 C , N M M L . S V A R ( 17, 14) , O W A S T , O C A P , G R A D ( 3 , 6 0 , 2 A C O S T < 6 0 ) , X C O S T ( 3 , 6 0 i T C T ( 3 , 6 0 ) ,N N , N P R O O » C F (60) ,3NWRSL (3) , PMV(10 0,3) , PVINC( ICO, 3) , tlENOT ( 3,60 ) , SCOST (3,601

CUM INV = SVAR(6,14) + S V A R ( 7 , 14) + S V A R ( 8 , 14)UNOrP = CUMINV - TDV2

COMPUTE ALLOWABLE MAXIMUM ACCELERATED DEPRECIATION.

• CDEPR = 0.3 * CUMINV IF(COEPR.GT.TOINC) 2 , 3

2 TCDF.PR = TOINC GO TO 4

3 TCDE°R = CDEPR

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4 i f (unoep.lt.TonrPD ) tcdepp = unolpTFOIUC = TOINC - TCDEPP T0V2 = TDV2 + TCOFPR RETURN END

SUBROUTINE OEPL(BOEP,TOV3.CUKINV,EXDEV,PROFN.OEPLC>

THIS SUBROUTINE COMPUTES THE ANNUAL DEPLETION ALLOWANCE AND TAXES.

COMMON N A M E (2D),NULSL,NSIM,NSLOP,RRATE,F E D R ,P M T R .P I T R ,D E P L R ,N D A Y , 1CAPAC,CONS,CONG,NEXP.NOC,NMML,S V A R (17,14),0W A S T ,C C A P ,G R A D (3,60), 2 A C O S T (60) ,XCQST(3,60),TCT(3,60>,N N ,NPROO , C F (60).3 N W R S L (3),PNV(10 0,3),PVINC(10 0,3), B E N O T (3,60)♦S C O S T (3,60)

BDEP = INCOME BEFORE DEPLETION AND TAXESOEPLC = DEPLETION CLAIMEDFED = FEDERAL TAXPROVI = PROVINCIAL INCOME TAXPPQVM = PROVINCIAL MINING TAXTOV3 = CUMMULATIVE DEPLETION CLAIMED

AMOUNT = CUMINV + EXDEV

COMPUTE DEPLETION IF THERE IS POSITIVE INCOME BEFORE DEPLETION.

UNOEPL = AMOUNT - TOV3 ALLOW = BDEP * DEPLR BASE = UNDEPL * DEPLR I F (BASE.G T . ALLOW) 20,30

20 OEPLC = ALLOW GO TO 40 30 DEPLC = BASE

40 IF(UNOEPL.LT.OEPLC) OEPLC = UNDEPL

COMPUTE THE TAXES.

FED = (BDEP - OEPLC) * FEDR PROVM = BDEP » PMTR PROVI = (BDEP - OEPLC) * PITR TAXSUM = FED *■ PROVM «- PROVI IF (TAXSUM.GT.BDLP) GO TO GO PROF N = BDEP - OEPLC -TAXSUM TDV3 = TDV3 ♦ DEPLC GO TO 99

90 PRINT 1GG,BDEP,FED,PROVM,PROVI 100 FORMAT(//10X,’ LOGIC E RROR*,4FI2 . 4 1

PROF N = 0 . 0 99 RETURN

END

SUBROUTINE NET P R V (P V ,N O )

THIS SUBROUTINE COMPUTES THE NET. PRESENT VALUE.

COMMON N A M E (20) ,NULSL, NSIM, NSLOP, R R A T E , F E D R , P MTR,PITR,DEPLR,NDAY,

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1 C A P A C ,cons,n C N 0 , N E X P , H O C , N M M L , S V A R ( 1 7 , 1 4 ) . O W A S r , O C A P , G R A O ( 3 , 6 C ) , R A C O S T (GO ) , X C O S r (3,F»0> , TCT (3, 60 I t N N t N P R O O t C P (f,3) ,1 N W R S L (3), P M V ( 10 0, if , VI NC ( 100, 3f , 13EN0T ( 3 , 6 0 ) . S C O S T (3,60) C O M M O N / R U N / N T A X,f j9 U G , N P L O TP V = 0,0 OO 60 KK = 1 ,NO 60 R V = P V + C F ( K K ) * ( l . / ( ( l . ^ R R A T E ) V * K K ) )I F ( N 9 U G . G T . 0) 1 5 , 2 0 15 P R I N T 1 0 , PV10 F O R M A T ( 1 C X , * N P V = * , F 1 2 . 0 )

20 R E T U R N E N D

S U B R O U T I N E O C F R O l (L ,R O I )T H I S S U B R O U T I N E C O M P U T E S D I S C O U N T E D C A S H F L O W R A T E OF R E T U R N D I S C O U N T E D C A S H F L O W I S D E F I N E D AS THE ^ D I S C O U N T R A T E * AT W H I C H T W O P R E S E N T W O R T H S O F T O T A L P O S I T I V E A N D N E G A T I V E C A S H F L O W S A R E E Q U A LD I M E N S I O N P I N ( 6 0 ) , P O U T (60)D I M E N S I O N W O R T H (5) , T V E S T (5 > ,C O M P ( 5 )COMMON NAME (20) ,N U L S L ,N S I M ,N S L O P ,R R A T E ,F E O R ,P M T R ,P ITR,DEPLR,NOAY,

lCAPAC,CONS,CCNO,NEXP,NOC,NMML,SVAR(17,14),0WAST,0CAP,GEAD(3,6C>, 2 A C O S T (60),X C O S T (3,60),T C T (3,60),N N ,N P R O D ,C F (60),3 N W R S L ( 3 ) , P N V ( 1 0 0 , 3 ) , P V I N C ( 10 0 , 3 ) , O E N O T ( 3 , 6 0 ) , S C O S T (3, 60)C O M M O N / R U N / N T A X , N B U G , N P L O T D A T A N H O S K , H O S K R T / C , 0/NU = NN + N P R O D J T I M E = N O DO 65 KK = 1 , NO I F ( C F ( K K ) ) 6 0 , 6 0 , 6 1

60 P O U T (KK) = - C F (KK)P I N ( K K ) = 0.0G O TO 65

61 P I N ( K K ) = C F ( K K I P O U T (K K ) = 0.065 C O N T I N U E

B E G I N D I S C O U N T E D R A T E O F R E T U R N C O M P U T A T I O N IN T = T R I A L D I S C O U N T R A T E ... N O F R A C T I O N A L P E R C E N T A G E T O L = T O L E P A N C E B E T W E E N P O S I T I V E A N D N E G A T I V E C A S H F L O W S K E Y A N D N KEY A R E S W I T C H E S F O R G O I N G T H R O U G H P R O P E R L O O P R= (1.04-DISC)P I N ( I ) = I - T H Y E A R P O S I T I V E C A S H INP O U T ( I ) = 1 - T H Y E A R N E G A T I V E C A S H O U T L A YC O M P ( K ) = D I S C O U N T p A T p B E I N G S T O R E D F O R C O M P A R I S O NW O R T H ( K ) = TOT AL P O S I T I V E C A S H F L O W S AT A G I V E N D I S C O U N T R A T ET V E S T ( K ) = T O T A L N E G A T I V E C A S H F L O W S AT A G I V E N D I S C O U N T R A T EP C A S H = F I N A L , T O T A L P O S I T I V E C A S H F L O W AT T H E I N T E R N A L R O I R A T ET N C A S H = F I N A L T O T A L N E G A T I V E C A S H F L O W AT T H E I N T E R N A L R O I RA T ER O I ( L ) = T H E I N T E R N A L ROI F O R L - T H S I M U L A T I O N .C H E C K IF U N O I S C O U N TC D T O T A L P O S I T I V E C A S H F L O W IS G R E A T E R T H A N T O T A L N E G A T I V E C A S H F L O W SN E G R O I =0

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106

S H I N = 0 . 0 S P O U T = 0 • C 00 1 1 = 1, JTIHE"SPIN=SPIN + PIN(I )1 S P 0 U T = S P O U T «-P0UT (I )I F ( S P I N - S P O U T ) 2 , 2 , 6

2 W K I T E ( 3 , 1 0 1 ) L1 0 1 F O R M A T C / 1 C X , * T H E V E N T U R E IS NOT W O R T H C O N S I D E R A T I O N - - S I M U L A T I I O N R U N N O = * , 1 5 1 R O I = - 0 . 0 N E G R O I = N E GR 0 1 1G O TO 99 ,

S E T T H E S T A R T I N G T R I A L D I S C O U N T R A T E AT 15 P E R C E N T6 T N T = 1 5

T 0 1 = 1 0 3 . 0 K E Y = 1 N K E Y = 1B E G I N N I N G OF A P P R O X I M A T E D I S C O U N T R A T E C O M P U T A T I O N

7 D I S C = F L 0 A T ( I N T 1 / 1 0 0 . 3U P P E R A N D L O W E R L I M I T S ON R O T ARE N O W B E I N G C H E C K E D .F I R S T C H E C K IF L O W E R L I M I T I S R E A C H E DI F ( D I S C ) 4 5 , 4 6 , 4 7

45 W R I T E ( 3 , 1 2 9 ) L G O TO 994 6 I F ( N K E Y - 2 ) 4 8 , 5 0 , 4 8L O O P 49 I N D I C A T E S T H A T L O W E S T P O S S I B L E R . O . I . IS Z E R O

49 ROI = 0.0 G O TO 994 8 I F ( K E Y - 1 ) 4 5 , 4 9 , 4 5

50 I A D D = 1P C A S H = S P I N T N C A S H = S P O U T G O TO 18C H E C K IF U P P E R L I M I T IS R E A C H E D

47 IF ( D I S C - 1 . 5 1 3 1 , 3 1 , 3 2 32 W R I T E ( 3 , 1 2 9 1 L

1 2 9 F O R M A T ( 1 H 1 , * L 0 G I C E R R O R IN P . W . C O M P U T A T I O N ... N S I M = *,1 5) G O TO 99 31 P P = 1 . 0

r = (i • o + n i s c *N O W C O M P U T E P R E S E N T W O R T H OF T O T A L P O S I T I V E A N D " N E G A T I V E C A S H F L O W SP C A S H = 0 . 00 0 8 N K = 1 , J T I M Er p = p p * R

8 P C A S H = P C A S H + P I N ( N K ) / P P

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107

Pp=l.0T NCAS H - P O U T (1)D O 0 I K = ? i J T I M F pp=pp»?

9 TNCASH=ThCA5H*P0Ur(NK)/PP

NOW COMPARE TOTAL POSITIVE. CASH FLOWS WITH TOTAL NEGATIVE CASH FLOWS

IF (ABS(PCASH-TNCASHI-TOL1 10,10*11 13 POI = I NT

GO TO 99 11 IF (PCASH-TMCASH ) 12,1?,13

I N C R E A S E I N T E R E S T R A T E F O R L O O P N O . 13 A N D D E C R E A S E F O R L O C P N O . 1213 I F ( K E Y + N K E Y - 2 ; 1 5 , 1 4 , 1 514 K E Y = 215 I F ( N K E Y - l ) 1 7 , 1 6 , 1 716 I N T = I N T + 5

G O TO 717 I A D O = 1 G O TO 18S T A T E NO. 18 IS T H E L O O P F O R C O M P U T I N G P . W . F O R 4 M O R E T I M E S

12 IF ( K E Y * N K E Y - 2 ) 2 0 , 1 9 , 2 019 N K E Y = 220 I F ( K E Y - 1 1 2 2 , 2 1 , 2 221 I N T = I N T - 5 G O TO 7.22 I A O D = - l

B E G I N N I N G OF F I N E R D I S C O U N T P A T E C O M P U T A T I O N18 k O R T H ( l ) = P C A S H T V E S T ( 1)= T N C A S H

C O M P ( 1 1 = INTDO 26 IC = 2,5

26 W O R T H (IC)= C •3 DO 23 IC =2,5 INT=INT + 1 ADD DIN T = IN T DISC=ni.NT/lC0. 0 P P = 1 . 0R = ( l . O f O I S C )DO 24 N K = 1 , J T I M E P P = P P * r

24 W O R T H (I C ) = W O R T H ( I C H P I N ( N K ) Z P P P P = 1.3T V E S T ( I C ) = P O U T ( 1 )DO 25 M < = 2 , J T I M EP P = P P * R

25 TVEST(IC)=TVFST(IC)+POUT(NK)Z P P23 C O M P ( I C ) = I N T

N O W B E G I N C O M P A R I S O N OF D I F F E R E N C E S A M O N G T O T A L N E G A T I V E C A S H

OOO

OOOO

OOO

O OOO

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108F L O W S A N D T O T A L t’O S T T T V t C A S H F L O W SS M A L 1 = A B S ( W O D T H ( 1 ) -T VE S T C1))NT 1 = 1S M A L ? = A H S ( W O R T H ( 2 1 - T V E S T (2))NT 2 = 2T F ( S M A L 1 - S M A L 2 * 3 5 , 3 5 , 3 6

36 S I 0 P 1 = S M A L 1 N T 0 T 1 = N T 1 S M A L 1 = S H A L 2 NT 1 = N T 2 S M A L 2 = S T 0 » 1 N T 2 = N T 0 T 1N A R R O W T H E I N T E R V A L TO THE N E A R E S T P E R C E N T

35 00 30 I C = 3,5O E L = A B S ( W O R T H ( I O - T V E S T (IC) )I F ( S M A L 1 - 0 E L » 3 7 , 3 7 , 3 f t

3ft ST 0 R 2 = S T 0 » 1 N T 0 T 2 = N T 1 S M A L 1 = 0 E L N T 1 = ICS H A L 2 = S T 0 R 2 N T 2 = N T O T 2 GO TO 30C H E C K IF N E W D I F F E R E N C E * 0 E L * L I E S IN B E T W E E N

37 IF ( S M A L 2 - O E D 3 0 , 3 0 , 3 939 S M A L 2 = O F L N T 2 = I C30 C O N T I N U E

A D D UP T O T A L D I F F E R E N C E IN P R E S E N T W O R T H D U E TO O N E P E R C E N T D I F F E R E N C E IN R A T EO I F F E R = S M A L l + S M A L 2I F (C O M P ( N T 1 > - C O M P ( N T 2) ) L Q , 4 5 , 4 140 P O I P E R = C O M P ( N T l ) + S M A L 1 / O I F F E P G O TO 4241 R O I P E R = C O M P ( N T 1 ) - S K A L I 7 D I F F E RT R U N C A T E C O M P U T E D ROI T O N E A R E S T T E N T H OF O N E P E R C E N T

42 P C A S H = W O F T H ( N T l >T N C A S H = T V E S T ( N T H I K 0 I = R0IF'EP»1 0 . G R O I = F L O A T ( T R O I t Z 1 C .I F ( N B U G . G T . 01 6 2 , 9 9

62 P R I N T 5 5 , ROI55 F O R M A T ( 1 C X , * D C F R 0 I = * , F 7 . 3 )99 R E T U R N E N D

SUBROUTINE WELGR(WGR)

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1'09

T H I S S U H R O U T I N F C O M P U T E S T H E W E A L T H G R O W T H P A T E .C O M M O N N A M E ( 2 0 ) , N U L S L , M S I M , N S L O P , R R A T E ,F F O R , P M T R ,P I T R , 0 E P L R , NO A Y , 1 C A P A C ,00fJ3, CCfvO, NE X P , N O C , N M M L , S V A R ( 17 . 1 4) , O W A S T , O C A P , G R A O ( 3, 6 0 1 ,

2 A C O S T ( 6 G ) , X C O S T ( 3 , 6 0 ) , T C T ( 3 , 6 0 ) , N N ,N P R O O ,C F (60) ,3 N W R S L (3), PM V (100 . 3) . PVI NC ( 12 0, 3) , 13ENOT ( 3 , 6 3 ) , S C O ST (3, 60 )C O M M O N / R U N / N TAX, N (3 U G , N P L O T NO = NN 4 N P R O O F I N V = 0 . 0 no 2 5 2 K K = 1 , N N 2 5 2 F I N V = F I N V + C F ( K K ) * 1 . / ( ( 1 . + R R A T E ) * * K K )I S S = NN + 1n o 2 5 4 KK = I S S ,NOI F ( C F ( K K ) ) 255,255,256

2 5 5 F I N V = F I N V «- C F ( K K ) * l . / ( ( l . + R R A T E l * * K K I G O TO 25 42 5 6 I F ( K K - N O I 2 5 7 , 2 5 9 , 2 5 92 5 7 IS = KK G O TO 2 5 82 5 9 F V = l.C F I N V - - F I N V

G O TO 4 0 0 22 5 4 C O N T I N U E2 5 8 FV = 0.3N C = NO - 1H O 260 KK = I S , N C260 FV = FV * C F ( K K ) * ( 1. 4-RR A T E > * * I N O - K K )F V = F V + C F ( N O )

F I N V = - F I N VIF (FV - F I N V ) 4 0 0 2 , 4 0 0 3 , 4 0 0 5 4 0 0 5 F L W G R = . A L O G 1 0 ( F V / F I N V ) / F L O A T ( N O )

W G R = 1 3 . 0 * * F L W G R - 1.0 G O TO 160 4 0 0 3 W G R = 0.0 G O TO 16 C4 0 3 2 F L W G R = A L O G 1 3 ( F I N V / A 3 S ( F V ) ) / F L O A T ( N O )W G R = - ( 1 0 . Q * * F L W G R - 1 . 0>160 I F ( N B U G . G T . O ) 1 0 , 2 0 10 P R I N T 1 7 0 , WGR 170 F O R M A T ( 1 0 X , * W G R = * , F 7 . 3 )

20 R E T U R N E N D

SU3R0UTINE S O R T ( N R E C , M A X , ARRAY)THIS SUBROUTINE SORTS THE ONE DIMENSIONAL ARRAY INTO INCREASING

ORDER VIA THE SHELL ALGORITHM.

INTEGER ARRAY(MAX)

NREC = NUMBER OF RECORDS TO SORT.MAX = MAXIMUM SIZE OF THE ARPAY.ARRAY = AN INTEGER ARRAY OF DIMENSION *MAX*.NOTE THAT NREC IS .LE. MAX.

1 = 1 1 I = 2*1

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110TF(I.LF.NRFC) GO TO 1

2 I = (1-1)/2 I F d . c 9 . 0 1 ȣTIJPN ITOP = NP.EC - I 00 10 J = l.ITOPK = J

3 1 = K ♦ II F (ARRAY(K).L E .ARPAY(L ) ) GO TO 10 ITE'IP = ARPAY(L)A R R A Y (L) = ARRAY(K)ARRAY(K) = ITEMPK = K-IJ F ( K . G T . O ) GO TO 3

10 CONTINUE GO TO 2 END

S U B R O U T I N E P S O O I S (01 S . M ,N S I M )T H I S S U B R O U T I N E C O M P U T E S T H E P R O B A B I L I T Y D I S T R I B U T I O N OF T H E G I V E N C E C I S I O N C R I T E R I A .D I M E N S I O N DIS C ICC) . B A S O (25) . P R O B ( 2 3 ) ,C P R ( 2 3 ) , P R G R ( 2 5)C O M M O N Z R U N Z N T A X . N B U G . N P L O TG O TO ( 4 0 , 5 0 , 6 0 ) M40 P R I N T 4141 F O R M A T (1 1 X , * P R 0 B A B I L I T Y O F A C H I E V I N G AT L E A S T ♦ Z 2 0 X , * T H 6 V A L U E

1 S H O W N * , 2 0 X , * I N C . N P V V A L U E ’ Z)G O TO 550 P R I N T 5151 F O R M A T ( 1 H 1 , 1 C X , * P R 0 0 A B I L I T Y OF A C H I E V I N G AT L E A S T * / 2 0 X , * T H E VA

1 L U E S H O W N * , 2 0 X , ♦ I N C . O C F R O I V A L U E * Z )G O TO 560 P R I N T 6161 F O R M A T ( 1 H 1 , 1 0 X , " P R O B A B I L I T Y OF A C H I E V I N G AT L E A S T * Z 2 0 X , * T H E VA

1 L U E S H O W N * , 2 0 X , " I N C . W G R V A L U E * Z )5 A I N T = ( D I S ( N S I M ) - D I S ( 1 ) ) Z 2 0 .0

0 0 10 I = 1, 2 3R A S O ( I ) = O T S ( l ) + ( 1 - 2 ) * A I N T K = 00 0 20 IS = 1 , N S I M I F d . E Q . 1 1 3,4

3 C P R ( I ) = 0.0 G O TO 23 ' 4 I F ( I . E 0 . 2 3 1 1 5 , 2 5

15 C P R ( I ) = 1.0 GO TO 23 25 I F ( I . E 0 . 2 t 7,6 7 I F ( O I S ( I S ) . F Q . B A S O ( I > ) 1 1 , 1 26 J F ( O I S d S ) . G T . 3 A S 0 ( I - i ) . A N O . O I S ( I S ) . L E . B A S D d ) ) 1 1 , 2 011 K = K * 1

20 C O N T I N U E12 P R O D ( I ) = F L O A T ( K ) Z F L O A T ( N S I M )I F d . E O . 1 1 2 1 , 2 221 C P R (I ) = P R O B ( 1 1

G O ro 2 j22 C P R (I ) - C P D ( T - l ) «• P ^ O O d )23 P k G R ( I ) = 1. - C P R ( I )P R I N T 7 0 , P R G P ( T ) , R A S O ( I )73 FOR.1AT (F30. 3 , F 3 3 . 3)10 C O N T I N U E

203 R E T U R N F NO

APPENDIX EINPUT DATA AND OUTPUTS OF THE FINANCIAL RISK

ANALYSIS. MODEL

112

«*- INPUT DATA —

p r o p e r t y - m a r g i n a l m i n i n g c o . o f Ca n a d a - f i n a n c i a l a n a l y s i s

FIXED VARIABLES

ULTIMATE SLOPE ANGLE

45

NUMBER of SIMULATIONS

100

NUMBER OF WORK.SLOPE

NUMBER OF WORK.DAYS/YR

350

PRE-PRODo PERIOD

8

EXPLORATIONPERIOD

YR.FOR WATER AND LAND AO.

YR.FOR MINE AND PLANT CONS.

RATE OF RETURN

,150

FED.INCOME TAX RATE

<>210

PROV.MINING TAX RATE

.100

PROV,INCOME TAX RATE

.150

DEPLETIONRATE

.330

CONC.GRADE (SULPHIDE)

* 250

OEM,COPPER GRADE

OXIDE ORE I N THE WASTE

CAPACITY OF THE LEACH.PLANT/DAY

MILLCAPACITY/DAY

PROD,YEAR

25

,800 .100 5000. 25000,

s t o c h a s t i c v a r i a b l e s -

EXPLORATION COST (S)

CONSTANT

VALUE = ' 5 0 0 0 0 0 , 0 0 0

ROYALTY (PERCENTAGE)

c o n s t a n t

VALUE = ' , 1 0 0

ORE GRADE - OXIDE

CONSTANT

VALUE = , 0 0 3

RECOVERY = SULPHIDE ORE

CONSTANT

VALUE = , 9 0 0

RECOVERY - OXIDE ORE

c o n s t a n t

VALUE = , 7 0 0

CAPITAL EXPENDITURE - MINE

c o n s t a n t

VALUE = 3 0 0 0 0 0 0 , 0 0 0

SALVAGE VALUE ( $ )

c o n s t a n t

VALUE = ■ • , 0 0 0

WORKING CAPITAL ( $ )

CONSTANT

VALUE = , 0 0 0 .

PRICE OF COPPER (S /TON CU)

CONSTANT

VALUE = 1 0 0 0 , 0 0 0

M ILL ING COST (S/TON ORE)

CONSTANT

VALUE = , 5 0 0

LEACHING COST (S/TON ORE)

c o n s t a n t

VALUE - , 5 0 0

116

CAPITAL EXPENDITUKE ~ MILL ($)

c o n s t a n t

VALUE = 2 0 0 0 0 0 0 0 . 0 0 0

CAPITAL EXPENDITURE - LEACHING PLANT (5.)

CONSTANT

VALUE = 1 0 0 0 0 0 0 0 . 0 0 0

WATER + LAND A Q U I S I T I O n COST ( $ )

CONSTANT

VALUE = 1 0 0 0 0 0 0 , 0 0 0

p o s t c o n C o Po s t < $ / t o n c o n c . )

c o n s t a n t

VALUE = 4 , 0 0 0

POST LEACH. COST ($ /T O N CEM. COPPER)

CONSTANT

VALUE = 5 , 0 0 0

MISCELLANEOUS COST ($ /T O N ORE)

CONSTANT

VALUE = , 0 0 0

WORKING SLOPE ANGLE TO BE TESTED = 25'35, 0 DEG

3. ORE GRADE - SULPHIDE

. WORK.SLOPE ANOLEas .000 .000 .000 .000

,007 .007 .007 x .007as .000 .000 .000 .000

.007 .007 .007 .007

GRADE FOR p r o d u c t i o n YEARS. 1 THROUGH 25000 .000 .000 .000 .007 .007007 ,007 .007 .007 .007000 .000 .000 .000 .007 .007007 .007 .007 .007 .007

.007 .007 .007 .007 .007 .007

.007 .007 .007 .007 .007 .007

117

Intermediate Results for One Simulation

— i n t e r m e d i a t e r e s u l t s—

MARGINAL MINING CO. OF CANADA - FINANCIAL ANALYSIS

SIMULATION NO. = 1

WORKING SLOPE ANGLE = 25

CASH FLOWS FOR YEARS 1 THROUGH 33

■IU56G7» 16V404O3. 16L92260.lV74:3b9.

iiHV =uCFROI Z wvR z

—106697• 25635299. 17SG9244.

-194307o3. 1<«V72426.

21.900 .171

-106667, 20900565. 16517442. 19566419.

-500000. -500000. -21206731. -21377655. -21551749. 29711477. 26079206.20177561. 19629791. 19193116. 18633013. 10522300. 18839532. 1859353°.19108825. 16866960. 15651672. 18355796. 16084518. 18950827. 19916256.

WORKING SLOPE ANGLE = 35

CASH FLOWS FOR YEARS 1 THROUGH 33

—166667. 24129910. 17L455u5. 17^3553.

INlPV ZUCFROI = f«CR z

-1666o7• *22981776.16111594.

-12o3b091.2:213727,

24.500.175

-166667, 20754223. 18742135. 17049847.

-500000. -500000. -18824897. -18948062. -19073690. 32183030. 25083021.14494014. 20074455. 19809708. 19574070. 19356705. 17717704. 17297016.19096853. 18856480. 3491212. 18352195. 18082106. 1179829. 17921276.

119

iVO(<i< iNv Suvf’c I 10k1ca4b01 o y

1Uil1314 lb10 17 16 19 <u11^3242beiu272629.3 Vui3c6334Ju36373639HUHi424344 4b40 47HU49b'u

SorxTi-b Values

i«Pv-1566669 -372102 -32410b -165-417 152142 4 4966b 67173b 696169 1064682

1159094 1294269 1329320 1546163 1549143 1728654 x6o3266 1906229 IVbGnbb 1970323 2014436 2069692 cUbbHOb 2112787 21^0267 2138o72 2187 13 2203367 2506191 23v976l 232994 9 2348277 23b2055 2405793 2467230 260422 9 2053796 29 41693 296b43u 2970973 5U40bl2 3051454 bl70060 3236711 5241301 3564535 3395471 3bc.9493 5 O _• i) i 7 b 4016576 4909545

FRvl WSR

.400 .0001.1 oo .0011.200 .0011.500 .0021.500 .0021.600 .0021,700 .0021.900 .0031.900 .0031.900 .0031.900 .0032.000 .0032.000 .0032.100 .0032.300 .0032.vO0 .0032.500 .0032.500 .0032.4 00 .0032.400 .0032.400 .0032.400 .0042.400 .0042.400 .0042.500 .0042. b00 .0042.o00 .0042.500 .0042.600 .0042.600 .004'2.uOQ .0042.600 .0042.600 .0042.600 .0042.o00 .0042.600 .0042.o00 .0042.u0U .0042,700 .0042.700 .0042. 700 .0042.700 .0042.600 .0042.600 .0052.9UJ .0052.900 .0052.900 .0053.000 .0053.100 .0053.200 • 006

120

Probability Distribution of Increased Net Present Value for 35° Working Slope Compared to 25°

(Clean up Cost 1.25 Times the Unit Mining Cost)

PKOortBlLiTY OF ACHILVIiMG AT LEASTm u VALUE. SHOwN INC. N'PV V^LVE

1.000 , 9 8 0 . 9 6 0 . 9 6 0 . 9 3 0 . 9 4 0 . 9 2 0 . 9 0 0 . 6 6 0 . 6 4 0 . 7 6 0 . 7 2 0 «c 20

1913604.667 1 6 6 8 6 6 9 , 0 0 0 1 2 6 3 9 3 3 . - 9 3 8 9 9 7 . 0 0 9 —614061,906- 2 6 9 1 2 6 , 2 0 3

3 6 8 0 9 . 4 64 3 6 0 7 4 6 . 1 6 7 6 6 5 6 6 0 . 6 7 3

1 0 1 0 6 1 6 . 5 9 4 1 3 3 5 5 5 2 , 2 8 1 1 6 6 0 4 8 7 , 9 6 9 1 9 8 5 4 2 3 .6 6 ,7 2 3 1 0 3 5 9 . 3 7 5 2 6 3 5 2 9 6 . 0 6 2 2 9 6 0 2 3 0 . 7 5 0 3 2 6 5 1 6 6 , 4 57 3 6 1 0 1 0 2 . 1 6 7 3 9 5 b 0 3 7 . u 75 4 2 5 9 9 7 5 , 5 6 2 4564 9 0 9 . 2 3 0 4 9 0 9 6 4 4 , 9 3 7 5 2 3 4 7 8 0 . 6 2 5

. 4 2 0

. 5 2 0

. 2 6 0

.120 . 060

. 0 4 0

. u20

.020

.020

.000

Probability Distribution of Increased Net Present Value for 35° Working Slope Compared to 2 5° (Clean up cost 3.00 Times Unit Mining Cost)

H.tOuAbiLjiTY OF ACHiL'/lNO AT LEAST THE VALUE C-ihOfcN

i.000 .900 . 9 8 0 . 9 8 0 . 9 6 0 . 9 8 0 . 9 2 0 . 9 0 0 . t60 . 6 8 0 . 6 0 0 . 7 4 0 • 060 • b4U . 3 5 0 . 3 2 0 . 1 6 0 .100 . 0 6 0 .020 .020 .020 .000

IN C . NPV VALUE

- 1 0 7 3 4 1 6 0 . 2 5 0 - 9 9 1 4 1 3 6 . 2 5 0 - 9 0 9 4 1 1 6 , 2 5 0 - 6 2 / 4 0 9 4 . 1 2 5 - 7 4 5 4 0 7 2 . 0 0 0 - 6 6 3 4 04 9 . 6 7 5 - 5 6 1 4 0 2 7 . 7 5 0 - 4 9 9 4 0 0 5 . 6 2 5 - 4 1 7 3 9 6 5 . 5 0 0 - 3 3 5 5 9 6 1 . 5 7 5 - 2 5 3 3 9 5 9 . 3 7 5 - 1 7 1 3 9 1 7 . 2 5 0

- 6 9 3 8 9 5 . 1 2 5 - 7 3 6 7 5 , 0 0 0 7 4 6 1 4 n , 125

1 5 6 6 1 7 1 , 2 5 0 2 3 6 6 1 9 3 . 3 7 5 5 2 0 6 2 1 5 . 5 0 0 4 0 2 6 2 3 7 , 5 0 0 464 6259.025 5 6 6 6 2 8 1 . 7 5 0 6 4 6 6 3 0 3 , 5 7 5 7 5 0 6 5 2 6 , 0 00

122

Probability Distribution of Increased Net Present Value for 35° Working Slope Compared to 25° (Clean Up Cost1.25 Times the Unit Mining Cost and 25% Increase

Probability of Failure)

PROBABILITY OF rtCUIi-VlNO AT LFASTTliL VALUE 5! 'OWN I N C . NPV VALUE

1 * 0 0 0 - 3 2 ? 5 1 9 . 2 d 5• 9 6 0 • - 1 2 7 6 5 2 . 7 5 0• 93(5 67213.7157• 960 262 35 :0 .3 24• 6 C0 _ 4 5 6 9 4 6 . 6 5 9• 8 4 0 6 5 1 8 1 3 . 3 9 6• 7 8 0 8 4 6 6 7 9 . 9 5 0•64 0 3 0 4 1 5 4 6 . 4t>9• 6 2 0 1 2 3 6 4 1 3 . 0 0 0• b Q0 , 14 3 1 2 7 9 . 5 4 7• 5 6 0 z 1 6 2 6 1 4 6 . 0 7 3• 4 6 0 1 8 2 1 0 1 2 . 6 0 9•32 0 - 2 0 1 5 8 7 9 . 1 5 6•26 0 2 2 1 0 7 4 5 . 6 6 7•20 0 2 4 0 5 6 1 2 . 2 1 9• 1 6 0 2 6 0 0 4 7 8 . 7 5 0•16 0 2 7 9 5 3 4 5 . 2 2 1• 1 2 0 2 9 9 0 2 1 1 . 8 4 4•0 6 0 3 1 8 5 0 7 6 . 3 7 b•0 6 0 3 3 7 9 9 4 4 . 9 0 6•0 4 0 3 5 7 4 8 1 ) . 4 3 7•0 2 0 3 7 6 9 6 7 7 . 9 8 9•00 0 3 9 6 4 5 4 4 . 5 0 0

123

Probability Distribution of Increased Net Present Value For 35° Working Slope Compared to 25° (Clean up Cost3.0 Times the Unit Mining Cost and 25% Increased

Probability of Failure)PROBABILITY OF /.CHIu VJn G AT LEAST

THu. VALUE SHOWN I N C . NPV VALUE

1 . 0 0 0 - 0 5 0 3 5 9 0 . 6 2 5. 9 2 0 - 5 9 8 5 1 6 1 . 0 0 0. 9 0 0 - 5 4 uO7 7 1 . ^ 7 5.9%0 ^ - 4 9 4 ^ 3 6 1 , 7 5 0. 6 6 0 - . - 4 4 2 9 9 V ? 1. 125. 6 2 0 " - 3 9 1 1 5 4 2 . 5 0 0. 7 0 0 - 3 3 9 3 1 3 2 . R/B. 6 4 0 - 2 8 7 4 7 2 3 . 2 5 0. 6 2 0 - 2 3 5 6 3 1 3 . 6 2 5. 6 0 0 - 1 6 3 7 9 0 4 . 0 0 0. 5 2 0 ' - 1 3 1 9 4 9 4 . 3 7 5. 4 6 0 - 6 0 1 0 6 4 . 7 5 0. 3 4 0 - 2 6 2 6 7 5 . 1 2 5. 2 8 0 2 3 5 7 3 4 . 5U0. 1 6 0 7 5 4 1 4 4 . 1 2 5. 1 6 0 1 2 7 2 5 5 3 . 7 5 0. 1 6 0 1 7 9 0 9 3 3 . 3 7 5.120 23003/7.00 0. 0 6 0 2 6 2 7 7 6 2 . 6 2 5. 0 2 0 32 4 6 1 9 2 . 2 5 0. 0 2 0 3 8 6 4 6 0 3 . 6 7 5. 0 0 0 4 3 3 3 0 1 1 . 5 0 0. 0 0 0 4 9 0 1 4 2 1 . 1 2 5

124

Probability Distribution of Increased DCFROI for 3 5 Working Slope Compared to 2 5° (Clean up Cost

1.25 Times the Unit Mining Cost)

o

PROu A P I L I H OF ACHIEVING AT LEAST THE Va LVE Sn O.vH

1.000* 9b C .980 . 960 ,980 ,900 . 9 0 0 . 94 0 . 9 2 0 . 9 0 0 . 0 8 9 , 6 6 0 . 7 8 0 . 7 4 0 . 7 2 0 . 6 4 0

. . 460 , 2 4 0 . 1 6 0 «u6U . 0 4 0 .020• u O O

INC. DCF HOI VALUE

. 2 6 0

. 4 0 0

.5 4 0

. 6 8 0

. 8 2 0 .9o01.100 1 . 2 4 0 3 . 3 6 0 1 . 5 2 0 1 • 6601 , 6 0 0 1 . 9 4 0 2 . 0 8 0 2.220 2, 3o02 , 5 0 0 2 . 6 4 0 2 , 7 6 0 2 . 9 2 0 3 . 0 6 03 . 2 0 0 3 . 3 4 0

125

Probability Distribution of Increased DCFROI for 35° Working Slope Compared to 25° (Clean up Cost

3.0 Times the Unit Mining Cost)

PROo m B xL U Y Cl- ACHIEVING AT LEASTTHE V/tLuzi 1H C , DCFROI VALUE

J. .00U « 590.t80 - 2 .S00

-k.010- 1 . 7 2 0

.960 " -1.430

.940 -1.140• 940 .. -.050•900 -.560•&80 ' -.270 .600 .020•780 ,310•7&0 .600.660 ,690•620 3,160•620 1,4 70•400 1.760•260 2,050•180 . 2.340•080 2.o30•040 2.920•040 3.210• 0 00 3,500.000 3,790

126

Probability Distribution of Increased DCFROI for 35 Working Slope Compared to 25° (Clean up Cost 1.25 Times the Unit Mining Cost and 2 5% Increased

Probability of Failure)

,ABILITY OF ACHIEVING AT LFAST TML Va «~UE SHvWU •

1. 000 . 9 0 0 . van .uro.9 SO• 9o0 *960 . 9 6 0 . 8 6 0 .600 . 7 2 0 . 6 6 0• 460 . 4 6 0 . 3 0 0 . 3 0 0 . 2 4 0 .200 .100 . 0 6 0 . 0 4 0 . 0 0 0 .000

IN C . DCFROI VALUE1 .000 1.1001.2001 . 3 0 0 1 . 4 0 0 1 . 5 0 0 1 . 6 0 0 1 . 7 0 0 1 . 6 0 01 . 9 0 0 2.000 2.100 2.2002 . 3 0 0 2 . 4 0 02 . 5 0 0 2 . 6 0 0

. 2 . 7 0 02 . 6 0 02 . 9 0 03 . 0 0 0 3 . 1 0 03 . 2 0 0

127

Probability Distribution of Increased DCFROI for 35° Working Slope Compared to 2 5° (Clean up Cost 3.0 Times the Unit Mining Cost and 25% Increased

Probability of Failure)

PROBABILITY Or aCHILVihvi AT LEALT1 Hv_ VALUE Ll.OWis' I N C . nCFPOl VALUE

1 . 0 0 0. 9 3 0• 9 3 0 . 9 G C . 9 3 0 .9 3 0 . o C 0 .020 . 3 2 0 .620 . 5 6 0 . 5 2 0 . 4 4 0 . 3 2 0 . 2 6 0 .200 . 160 . 100 . 100 . 0 3 0• 0 2 0 .020 . 000

- . 9 w U - . 7 2 5 - . 4 7 0 - . 2 1 5

. 0 4 0

. 295

. 5 5 0

. 8 0 5 1 . 0 6 0 1 . 3 1 5 1 . 5 7 0 1 . 8 2 5 2 . 0 6 0 2 . 3 3 5 2 . 5 9 0 P . 845 3 .1 UU 3 . 5 5 5

2.000 3 . 7 4 5

128

Probability Distribution of Increased WGR for 35° Working Slope Compared to 25° (Clean up Cost 1.25 Times

the Unit Mining Cost

HROuAlULin OF ACHIEVING A1 luc VALUE. SHOWN

1.000.two. 9 6 0 . 9 6 0 . 9 6 0 . 9 4 0 . 9 4 0 . 9 2 0 . 9 0 0 .660 .600 .660 . 6 0 0 . 6 2 0 . 3 6 0 . 500 .200 . 100 • 060 .020 .020 .000 .000

LEASTIN C . V/GR VALUE

-.000 .000 .000 .001 .001 .001 .002 .002 .002 .002 , 0 0 3 . 0 0 3 . 0 0 3 . 0 0 4 , 0 0 4 , 0 0 4 , 0 0 4 , 0 0 5 . 0 0 5 . 0 0 5 ,00b , 0 0 6 . 0 0 6

129

Probability Distribution of Increased WGR for 35° Working Slope Compared to 25° (Clean up Cost 3.0 Times

the Unit Mining Cost)

HRluablLlTY OF ACHIEVING A1 The. VmLOc SH0.,iN

1 . 0 0 0 . 9 6 0 . 960 . 9 6 0 . 9 6 0 . 9 8 0 . 9 4 0 . 9 2 0 . 660• 66 u• 660 . Vo0 . 6 6 0 • 6 0 U . 4 6 0 . 3 4 0 . 2 6 0 . 1 4 0 . osu. 0 4 0 .020 .000

• . 000

l e a s tINC. WGR VALUE

- . 0 0 9 - . 0 0 5 - . 0 0 7 — .006 - . 006

" - . 0 0 5-.004- . 0 0 3 - . 0 0 3 -.002 -.001 -. 000 .000 .ooi .002 . 0 0 3 . 0 0 3 . 0 0 4 ,00b . 006 . 0 0 7 . 0 0 7 , 0 0 6

130

Probability Distribution of Increased WGR for 35° Working Slope Compared to 25° (Clean up Cost

1.25 Times the Unit Mining Cost and 25% Increased Probability of Failure)

PROBABILITY vr~ .xCHILVlNO AT LEAST

THL VAcUE SUOW.N INC..WGR value

i . ono. 9A0 • 960 . 9 0 0• 920 . B40 . 7 2 0 . 7 0 0 . 600• 60 0 . 6 2 0 . 5 0 0 . 4 4 0 .200 .220 . 1 6 0 . 100 .100 . 0 3 0 .060 . 060 . 000 • 000

.001

.002

.002

.002

.002

.002

.0 02

. 0 0 3

. 0 0 3

. 0 0 3

. 0 0 3• 0 0 v. 0 0 3. 0 0 4. 0 0 4. 0 0 4* 004 . 0 04 . 0 0 4 . 0 0 5♦ 0 0b . 0 0 5 . 0 0 5

Probability Distribution of Increased WGR for 35° •Working Slope Compared to 25° (Clean up Cost

3.0 Times the Unit Mining Cost and 25% Increased Probability of Failure)

PROJAi.'ILiTY OF ACHIr.VlNS AT l-'fASTt h l j a l ijr." s i io w i i INC. V!0R Va l u e

1. 000• 9 AO . 9 6 0• 960 .900 . BOO . 7 0 0 . 660 . 6 6 0 .sec• 0 .410 . 3 6 0 . 3 0 0. 2 6 0 .220 . 120 . 120 . 0 6 0 .020 . u20 . 000 .000

-.00b - . 0 0 4 - . 0 0 4 - . 0 0 3 -.003 -.002 -.002 -.001 -.001 -.0 00 .000 .001 .001 .002 .002 . 0 0 3 . 0 0 3 . 0 0 4 . 0 0 4 . 0 0 4 . 0 0 5 . 0 0 5 . 0 0 6

SELECTED BIBLIOGRAPHY

Black,

Brown,

Brown,

Coates

Gentry

Halls,

Hrebar

Jones,

Kim, Y

Kim, Y.

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J. L., "The Basic Economics of Open Pit Mining," Planning Open Pit Mines, Proceedings of the Open Pit Mining Symposium, Johannesburg, Republic of South Africa, 197 0, pp. 125-131.Matthew J. Ill, Business Risk Analysis Applied to Preliminary Economic Evaluation of Mining Proper­ties, -M.S. Thesis, The University of Arizona,Tucson, 1971.Cyril, "Economic Analysis for Mining Ventures and Projects," Surface Mining, A.I.M.E. New York, 1968, pp. 997-1013.C., Upadhyay, R. P., and O'Neil, T* J., A Benefit Cost Model for the Pit Slope Economics Study,College of Mines, The University of Arizona, Tucson, 1973.C., Williamson, G. B., and Sturgal, J. R., A Short Course on Mine System Simulation Using a Digital Computer,. Department of Mining and Geological Engineering, The University of Arizona, Tucson, 1973.

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Michelson, R. W., and Polta, H. J., "A Discounted Cash-flow Model for Evaluating the Cost of Producing the Iron Ore Pellets from Magnetic Taconite," A Decade in Digital Computing in the Mineral Industry, A.I.M.E., New York, 1971, pp. 211-240.

Moolick, R. T., and O'Neill, John E., "Stripping Methods Including Advance Stripping," Surface Mining, A.I.M.E., New York, 1968, pp. 180-182.

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Sasieni, M., Yaspan, A., and Friedman, L., Operation Re­search: Methods and Problems, John Wiley and Sons,Inc., New York, 1959 , pp . 58-69.

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