Alternative Methods for Economic Analysis in Potash David Vaughn Abstract The decision about when and where to make large capital investments is an important one for all corporations. The Mosaic Company has identified an investment opportunity in a satellite ore body related to its Carlsbad, NM operations. Based on internal economic analysis this project was determined to be on the borderline of an acceptable investment opportunity. Because of this status more analysis of this project is warranted. An alternative method for determining the parameters used in economic analysis are presented. These parameters include potash prices, production costs, and capital costs. The methods used for forecasting these parameters include Geometric Brownian Motion, assessing a beta distribution for modeling capital costs, and assessing a normal distribution with creep (inflation) for the production costs. These forecasts and models are then used as inputs into an economic model and an expected Net Present Value (E (NPV)) and Probability that the NPV>0 (P(NPV)>0) are calculated.

Acknowledgements This work could not exist without the potash price forecasting model built by Dr. Anselmo from the New Mexico Institute of Mining and Technology, who also contributed greatly to the author’s understanding of much of the subject matter present in this report. Also deserving of recognition are Dr. Mike Rahm and Terry Seal, for their salient information about Mosaic’s internal methods and for the data they provided to develop the alternative methods.

Introduction and Background Potash was discovered in the Permian basin through oil drilling in the 1925 and the first commercial shipment of potash followed in March of 1931. By 1934, 11 mining companies had become involved in potash mining in the Permian basin (Earth Matters, 2008). Currently two companies, Mosaic and Intrepid, operate 3 mines in the Permian basin. These companies produce 75% of U.S. Sales from their mines in New Mexico (USGS).

Mining and Processing: Several methods are utilized to extract potash ore including solution mining, room and pillar mining, and modified longwall mining. In New Mexico solution mining is in the early stages of being utilized while room and pillar mining is the primary method for ore extraction. Horizontal drum continuous miners are used to mine entries that range from 10 to 40 feet wide, with typical entries in the 30 ft range. Entries are mined on a grid pattern with pillars left for roof support. The ore is then brought to a hoist underground through belt systems and hoisted to the surface using either double drum or Koepe/friction hoists. Once on the surface two processing methods are used dependent on the ore type. For Sylvite (typically what is thought of as Potash) a flotation process is used to separate the ore from the waste product. For langbeinite (a specialty product only found in New Mexico) a heavy media process is used to float the waste and separate the ore. Once the ore has been separated it is put through a fluid bed dryer and compacted. Finally it is screened and separated by size fraction according to the different products being offered. Once the final processing is complete the product is shipped to a warehouse for storage until it is shipped on railcars for sale. From the warehouse the product is sold on seasonal campaigns called “fill” campaigns. Salesmen from the company fill contracts with various entities, typically large agricultural firms. The contracts are for a designated amount of product to be delivered by a designated time. For example, a large farm in Kansas may buy 10,000 tons of granular muriate product to be delivered by the end of November for a certain price. The price is largely determined by Midwest Warehouse prices for domestic sales and C & F Brazil prices for the Brazilian market. Large customers do negotiate the setpoint of the price but generally it is closely related to the two prices discussed. These two markets are the major consumers for New Mexican Potash. Payment for contracts is typically made once the product leaves the warehouse for delivery to the customer.

Executive summary of Proposed Capital Project The project being analyzed was once owned by the Noranda corporation and the namesake has been assigned to the deposit being evaluated. The Noranda deposit is located ~18 miles to the Northeast of Mosaic’s current Main Plant operations. This deposit represents a significant extension to Mosaic Carlsbad’s current operations. The major advantage of this deposit is its higher average grade.

Base Case economic Analysis To evaluate whether further investment in the Noranda project was warranted an AACE class 5 study was conducted to determine the capital costs at the scoping level as well as develop an initial timeline (for an explanation of what an AACE class 5 study is please see Appendix A). Based on this study the estimated capital cost was determined. Through further evaluation it was determined that some of the capital should be considered “shared” capital, or capital that would be spent whether the project took place or not. This capital money was primarily composed of mining equipment and belt and belt structure and was not included in the economic analysis. Another aspect determined by the scoping study was the timing of the capital expenditures. The first year would have a comparatively small capital expenditure for a higher level of study, followed another expenditure the second year, for feasibility level engineering including the initiation of an Environmental Impact Statement (EIS). This process is estimated to take 3 years. Major Capital expenditures then take place in years 5 and 6 respectively. The Mosaic company has an internal excel spreadsheet that is used to evaluated large capital projects. It should be noted that the highest production rate possible using the Wardrop study was chosen to accelerate the payback period for the project. This production rate was chosen because Mosaic's general strategy on projects is to undertake projects have faster payback periods when possible. The capital costs estimates for the base case are based on highest available rate. The incomes in this project are based on the expected price of potash. Three pricing scenarios are utilized in this analysis. All three cases were modeled using the internal spreadsheet. Also It should be noted that for this project Carlsbad expected sales are 25% domestic and 75% export. Based on the analysis done it was determined that the internal rate of return was very close to the minimum required rate of return to proceed, but did not quite meet it, and further analysis was warranted.

Methodology Three different factors were developed to offer an alternative analysis to the base case. These factors were potash price, capital cost, and production cost. A summary of the methodology used to develop an alternative for each of these parameters is presented below. Potash Pricing Model For the potash pricing model we begin with the Ornstein-Uhlenbeck Geometric Brownian Motion (GBM) model with mean reversion to generate 20 years of potash prices on a monthly basis. In general the formulation for a single period price change is: ( where

is lognormally distributed so that [

) (1) ]

[ ] (Anselmo, 2012). We can then

get the Ornstein-Uhlenbeck formulation (Anselmo, 2012): [ ((

)

√ )]

Where N is the normal distribution and T is the discrete-simulation time iteration number.The mean-reversion extension of the above expression is re-written in terms of mean (

) and standard deviation

√

(Anselmo, 2011). The GBM parameters ,

the mean-reversion parameter, and , the value to which the process reverts, and also

may

then be estimated via AR(1) regressions (Dixit and Pindyck, 1994). Based on initial work done by Dr. Peter Anselmo to analyze West Texas Crude Spot prices, we now present a modification of the Dixit and Pindyck process based on the working hypothesis that distinct sub-patterns in the price data exist, and may be modeled and identified via the AR(1) regressions done on moving data windows. Thus parameters

and

over time, and should be estimated on a dynamic basis during simulation.

and

may change

If historical time series data are used to estimate GBM-MR parameters, one standard procedure for fitting the parameter m is via an AR(1) regression of log returns for the price stream (Anselmo, 2012). We define

( ), and m is estimated from the regression

equation (3) with

(

and

) (Dixit and Pindyck, 1994).

A summary of the potash price data is found in Appendix A. As with Anselmo’s Oil data the hypothesis is that there are significant linear patterns in sub-sections within the data. These sub-sections can be associated with changing values of ,and parameters

and

and

. The selection of the

for forecasting is then achieved by looking at historical data and

determining what past events, or data windows, are likely to be repeated in the future. One specific example of this is supply/demand dynamics. A great level of analysis has been done on future demand for potash, it can be easily found on major potash producers’ websites as well as from publication from the International Fertilizer’s Association (IFA). There have also been a number of academic studies conducted on this subject. In addition a survey of industry activity gives a good picture of the future supply timeline. When you combine these two you get a picture of the level of surplus that is likely in the future and can compare to how the market reacted in the past to similar market conditions. From this information

and and

are

selected based on an expert assessment of the historical subsections for forecasting. In general the idea is that a significant linear subset of historical data, or scenario, is analyzed and their parameters are defined. These scenarios are then used, and/or combined or modified, to generate price forecasts based on input from a knowledgeable end user. The model can then be used, because of the included error term, to generate simulated price time series that can be used in cash-flow simulations. Capital Cost Estimation Model For estimation of the Capital costs involved in this project a beta distribution was chosen to represent each of the major capital sectors within the project. In all three beta distributions

were used based on the level of confidence given to a specific sector. For example, because mining equipment has a well understood cost it’s risk level was low and it was modeled with the “low risk level” beta distribution. A summary of capital costs, their chosen risk levels and a summary of the parameters used in the beta distributions is in Appendix B, table B2. In comparison to the capital costs reported by Wardrop the costs estimated by the beta distributions were, in general, lower (Wardrop, 2011). This is due to several factors. One is that each capital cost was analyzed and the understanding of that cost was factored into a probabilistic distribution. This is in contrast to a blanket addition of 40% contingency applied in the Wardrop study. For example, because the equipment that will be purchased is the same as the equipment used in current mining operations, the cost of that equipment is well understood and a 40% additional contingency is not needed, instead that cost is modeled with a beta distribution that produces a capital cost based on the base cost in the Wardrop study with a 95% chance that the cost will be within +/- 10% of that base cost. The alternative method was developed in response to the general idea that the probability of a 40% overrun is, in reality, pretty small, however smaller overruns between 0% and 40% are more likely. In this way the inputs from the Wardrop study, combined with expert knowledge, were used as a basis for the development of beta distributions for the capital costs. Production Cost Estimation Another aspect of the Base Case model that was modified is the estimated production costs. In the base case model these costs are held constant at produced a calculated nominal rate. This cost is based on an average of the last 6 months cost/ton for Mosaic Carlsbad’s Muriate product. As an alternative to this method, the production costs were modeled as a normal distribution with the mean and standard deviation determined by 3 years worth of production cost data. These costs also had an inflationary factor of 2% added, which is the same inflationary factor used in the Base Case analysis. A summary of the parameters used in the production cost model can be found in Appendix B. In general the model predicts higher production costs than the base case model due to the addition of the inflationary factor included.

Analysis Potash price forecasts were produced using supply and demand scenarios for potash until 2030 as well as supply and demand scenarios for oil (which has a linear correlation of .85 with potash price). The oil scenarios were used as predictors of potash price. So if oil supply/demand was “tight”, then potash price was predicted in the “tight” scenario of the model. The linear subset length was chosen by analyzing which length was most sensitive to changes in the market with the greatest confidence interval. In other words the “window” length that recognized significance in potash price changes the best. This length was determined to be 14 data points long with a confidence interval of 99.5%. The

and and

factors are then chosen by

analyzing similar supply/demand scenarios from historic data, Figure 1 shows historic price data with the corresponding backfit prices created using the model. A summary of the capacity and demand scenarios and the corresponding

and

and

parameters used to construct the life-

of-project scenarios for each trial can be found in Appendix C. There is a caveat in that it must be accepted that a fundamental shift has occurred in potash (and oil) prices, but this notion has been generally accepted by numerous experts in the field. This is mentioned because the predicted surpluses go beyond historic levels but prices are not predicted to reach the historic prices associated with these levels, instead, because of the shift, more recent prices/surpluses are used for prediction of price. This may be because of the significant increase in demand that is predicted, due to the rapid GDP growth (and corresponding increase in food consumption) in China and India in the coming decades.

1200

1000

800

Price

600

Back Fit Back Fit 2 400

200

1990-01 1990-11 1991-09 1992-07 1993-05 1994-03 1995-01 1995-11 1996-09 1997-07 1998-05 1999-03 2000-01 2000-11 2001-09 2002-07 2003-05 2004-03 2005-01 2005-11 2006-09 2007-07 2008-05 2009-03 2010-01 2010-11 2011-09

0

Figure 1: Summary of historic price Data with backfits created by model Also the supply scenario presented in Appendix A is based on known expansion projects within the potash industry as well as current Greenfield projects (A Greenfield project is a project that has no infrastructure, basically starting from a “green field” and building everything required to undertake mining, processing, and transport to market of a resource. In potash they have an estimated completion time of 8 years). In addition, beyond the year 2020 industry capability was predicted by the author using an educated guess. A summary of each pricing scenario is as follows: Trial 1: Potash demand will increase at the rate described by H.Magan of the international potash institute for a potassium:nitrogen ratio of 0.25 (IPI, 2005). This rate is approximately 1,242

million tons KCl each year. Potash capability will follow what is predicted in Appendix C. The breakdown of how the pricing scenarios are expected the fall is as follows: 

from 2012-2013 market conditions are expected to be similar to 2010, that is to say there is nominal supply and demand conditions



from 2014-2018 market conditions are expected to be similar to 2007 or in a condition of oversupply



2019 returns to nominal conditions as demand increases faster than supply once again market conditions are expected to be similar to 2010



For 2020, Several large projects that are currently in the pipeline begin ramping up and industry capability once again outpaces demand, market conditions are similar to 2006



The large projects reach full production in 2021 and 2022 and there is a glut of potash on the market, market conditions are worse (from a producers standpoint) than 2006



From 2022-27 industry capability slowly increase but demand increases at a higher rate and market conditions are similar to 2007



From 2028-2030 several other large projects that were started in 2020 ramp up and come online and once again there is a glut of potash, market conditions are worse than 2006

Trial 2: Potash demand will be at the rate described by H.Magan of the international potash institute for a potassium:nitrogen ratio of 0.35 (IPI, 2005). This rate is approximately 2,075 million tons KCl each year. Potash capability will follow what is predicted in Appendix C. The breakdown of how the pricing scenarios are expected the fall is as follows: 

From 2012-2016 market conditions are nominal, current expansions are well paced with the rate of increase in supply, market conditions are similar to 2010



From 2017-2018 Demand outpaces industry capability as expansion project have been completed and no significant industry capability is added, Market conditions are similar to 2011



2019 is a year of tight supply, demand is very near industry capability and market conditions are similar to 2008



From 2020-2022 Large projects currently in the pipeline come online and capability makes gains on demand, Market conditions are similar to 2011



From 2023-2030 demand simply outstrips industry capability market conditions are similar to 2008

Trial 3: Potash demand is predicted to grow at 3%/year steadily based on predictions by Mosaic, Potash corp. etc. Potash capability will follow what is predicted in Appendix C (Potashcorp 2010 overview). The breakdown of how the pricing scenarios are expected the fall is as follows: 

2012 is a year of nominal market conditions similar to 2010



From 2013-2016 expansions create an oversupply situation as demand does not grow as fast as industry capability, market conditions are similar to 2007



From 2017-2022 demand grows slightly faster than industry capability but supply demand conditions remain nominal, market conditions are similar to 2010



From 2023-2024 no new large projects or expansions are coming online and industry capability growth is not able to keep up with demand growth, market conditions are similar to 2011



From 2025-2028 demand continues to challenge industry capability and supply becomes very tight, market conditions are similar to 2008



2028 large projects started in 2020 come online and ease supply tightness, but only slightly, market conditions are similar to 2011



From 2029-2030 with no new significant industry capability additions demand once again makes supply conditions very tight, market conditions are similar to 2008

Trial 4: The parameters for potash price forecasting are based on oil industry capacity/demand dynamics as described in OPEC’s 2011 annual report (OPEC, 2011). The premise of this trial is

that potash prices closely follow oil prices, so for this trial the supply/demand trend for oil is described until 2030 

From 2012-2013 oil demand/capacity is at nominal levels and prices are expected to be similar to 2010



From 2014-2018 Oil demand/capacity is expected to reflect an oversupply scenario and prices will be similar to 2007



From 2019-2021 Market conditions return to nominal and market conditions are similar to 2007



From 2022-2025 oil demand growth is greater than capacity growth and market conditions are similar to 2011



From 2024-2030 oil industry capacity is challenged to meet demand and very tight supply results, market conditions are similar to 2008

A summary of the forecasted prices is shown in Figure 2. It is evident that in all scenarios except Trial 1 demand to capability becomes tight several years before 2030, which is where the economic analysis stops. This, in turn, creates a forecast of high potash prices similar to those observed in 2008. Also a minimum of 12 month blocks were chosen for pricing scenarios since this is the level of detail presented in the Base Case Analysis.

1400 1200 1000 Trial 1

800

Trial 2 600

Trial 3 Trial 4

400 200

1 10 19 28 37 46 55 64 73 82 91 100 109 118 127 136 145 154 163 172 181 190 199 208 217 226 235

0

Figure 2: summary of forecasted potash price ($/ton KCl) The next parameter that was analyzed is the capital costs. As mentioned in the methodology section the capital costs were separated into categories according to the uncertainty associated with each one. A value of 1 was given to costs which had a high level of uncertainty and a beta distribution was developed to approximate a cost with a 95% confidence that the costs would fall within +39%/-18% of the mean. A value of 2 was given to costs which had a moderate level of uncertainty and a beta distribution was developed to approximate a cost with a 95% confidence that the costs would fall within +25%/-10% of the mean. A value of 3 was given to costs which had a low level of uncertainty and a beta distribution was developed to approximate a cost with a 95% confidence that the costs would fall within +10%/-10% of the mean. A summary of the parameters used for the beta distribution as well as a breakdown of the categorization of each of the capital costs can be found in Appendix C. The last parameter that was analyzed was the incremental cost/ton. This was done by analyzing the transportation costs from the remote mining site back to the current processing plant site and incorporating a percentage of existing product cost/ton with an inflationary factor. Also a cost/ton floor a cost/ton ceiling of were applied. Figure 3 is an example of one cost/ton scenario (many exist since it is determined by a normal distribution).

product cost/ton

Jan Sep May Jan Sep May Jan Sep May Jan Sep May Jan Sep May Jan Sep May Jan Sep May Jan Sep May Jan Sep May Jan Sep May

product cost/ton

Figure 3: simulated product cost/ton used in economic analysis Results All three of the parameters were implemented in an economic analysis spreadsheet and models were run for each of the 4 trial scenarios. The model iterates 1,000 times to produce NPV’s, then the probability that the NPV will be less than 0 – the probability of a negative outcome P(NPV>0) is calculated for a 12% discount rate. The results are presented in tables 1-4. An attempt was also made to mimic the base case potash price “expected case” scenario to compare results from the base case economic analysis spreadsheet. Table 5 summarizes the results from plugging forecasted prices into the economic spreadsheet used for modeling.

Mean std. dev P(NPV>0)

Trial 1 NPV $ (54,068.91)High Negative ~10% of mean NPV$ 4,678.53

Formatted Table

IRR N/A N/A

0% 301607.1135Slightly lower Average Capital Costs than Wardrop Study Table 1: Summary of results for Trial 1, NPV numbers in ,000s USD, because of the large periods of oversupply in Trial 1 the economics do not present a positive picture for investment in another potash mining operation. Trial 2 NPV IRR Very $ 109,460.41High Mean Positive 178% $ 4,570.96~5% of std. dev mean NPV 20% P(NPV>0) 100% Slightly lower than Wardrop Average Capital Costs Study300981.5104 Table 2: Summary of results for Trial 2, NPV numbers in ,000s USD, because of the long periods of tight supply especially as the proposed operation is ramping up this is the most positive of the trials with no probability of the NPV>0. Trial 3 NPV

IRR High Mean positive45083.34448 57% 4575.085677~5% of std. dev mean NPV 9% P(NPV>0) 100% Slightly lower than Wardrop Study Average Capital Costs 300124.8257 Table 3: Summary of results for Trial 3, NPV numbers in ,000s USD, even though trial 3 presents moderately conservative potash prices as the proposed project ramps up late stage supply tightening produces positive results for the project with P(NPV>0) equaling 100%. Trial 4

Formatted Table

NPV IRR 47374.88862High Positive 60% 4768.358164~10% of Mean std. dev NPV 10% P(NPV>0) 100% Slightly lower than Wardrop Average Capital Costs Study 301375.2964 Table 4: Summary of results for Trial 4, NPV numbers in ,000s USD, similar to the results in trials 3 this scenario presents positive results even with differing timing on the tightening of potash supply vs. demand. Once again P(NPV>0) is 100%. Mean

Mean std. dev P(NPV>0)

Base Case price forecast NPV $ (5,587.69)Slightly negative $ 4,667.28~same as mean NPV

Formatted Table

IRR N/A

N/A 8% Slightly lower than Average Capital Costs Wardrop301562.2404 Table 5: Summary of results for Base case price forecast input into modeling spreadsheet, NPV numbers in ,000s USD, interestingly in the base case outcomes from the alternative model present slightly better outcomes than those produce by Mosaic's internal economic analysis spreadsheet. This is largely due to decreased capital costs associated the alternative model as well as the less conservative timing of when those costs are applied. Conclusions: Comparing the Base Case Mosaic model to the model developed we can see that the model is actually more conservative using the same price forecast. The Mosaic model predicted and a negative NPV@12% of ($8,083,000) while the alternative model that mimicked the base case potash price forecast predicted a meansimilar negative NPV@12% of ($5,587,690) using 100 iterations of the model. It is also interesting to compare the range in results using the alternative modeling method for the four different trials. The three scenarios based on moderate to tight demand/capability dynamics give positive results for the project; it is only with the base case and the extreme oversupply that the project does not appear to be a good investment. Regarding the base case, pricing has already proved to be ~$100 greater than predicted for 2011. Also there are numerous multi-billion dollar projects within the potash

industry that won’t be going into full production until as late as 2020, this also supports the idea of very strong fundamentals within the industry. There are some issues that should be discussed with the discount rate as well. The 12% hurdle rate is based on projects that have generally low risk, and this may not be appropriate for the Noranda project. There are significant challenges associated with the project including an average mining depth that is significantly greater (1700-2200 ft vs. 500-1200 ft for current operations). Also there are significant occurrences of a mineral called Carnallite which negatively affects ground conditions in the mining operations as well as creates problems during processing. Even with all these challenges, the IRR’s predicted in the moderate to strong demand cases recommend proceeding with the project even when treating this as a high risk project. Another issue worth noting is the probability of one of the trials occurring vs. any of the other trials. One aspect of this model that is fairly predictable, at least until 2020, on the supply side, since new projects take a significant amount of time (8 years) to be brought online and an in depth survey of current industry projects was conducted. On the demand side the most recent research on the subject was done by Potashcorp in conjunction with IFA and this data likely reflects the most probable case of the trials, this case is represented by Trial 3. To address this, a decision tree was developed with probabilities heuristically assigned to the likelihood of each of the four trials as well as the modeled approximation of the bases case analysis using the model. The results are shown in Figure 5. The results of this analysis tell us that this project has an expected NPV@12% of $21,566,700.

Formatted: Font: 12 pt Formatted: Left

Figure 5: Decision tree of trials and base case E(NPV) is $21,566,700. Each arc of the decision tree represents the mean NPV from its respective trial. These mean NPV's are then multiplied by the probability of that scenario (determined by "expert user input"). The E(NPV) is then calculated as the sum-product of these probabilities and mean NPV's. It is shown under the "Chance" cell. Based on the analysis conducted using the decision tree the project was moderately favorable with a positive NPV. The key aspect of the alternative model is the ability of the user to analyze new information and update the model accordingly. In this way the alternative model is quite adaptable and better able to handle new information.

References Tenkorang, F. and Lowenberg-DeBoer J., Forecasting Long-term Global Fertilizer Demand, https://cours.etsmtl.ca/gol502/Notes%20de%20cours/globalfertdemand.pdf Anselmo, Peter., “Dynamic Regression Estimates of Geometric Brownian Motion Parameters”. working paper in the NMT Department of Management Dixit, Avinash K., and Pindyck Robert S., Investment under Uncertainty. Princeton University Press 1994 Potashcorp 2010 Overview., http://www.potashcorp.com/media/POT%202010_Overview_Complete.pdf BP Energy Report 2012 http://www.bp.com/liveassets/bp_internet/globalbp/globalbp_uk_english/reports_and_public ations/statisti cal_energy_review_2011/STAGING/local_assets/pdf/2030_energy_outlook_booklet.pdf OPEC 2011 Overview http://www.opec.org/opec_web/static_files_project/media/downloads/publications/WOO_20 11.pdf Potashcorp 1st Quarter Report 2011 http://www.potashcorp.com/media/POT_Q1_MAR_2011.pdf IFA report Production and Trade 2011 http://www.fertilizer.org/ifa/HomePage/STATISTICS/Production-and-trade Wardrop, Lea Lease Project Scoping Study Document No. 1050741300-REP-G0002-01 March 2011

Bibliography U.S. Potash price/ton: Source=http://minerals.usgs.gov/ds/2005/140/potash.pdf U.S. Corn price/bushel: source=http://www.farmdoc.illinois.edu/manage/uspricehistory/USPrice.asp U.S. Oil price/bbl: source=http://inflationdata.com/inflation/inflation_rate/historical_oil_prices_table.asp GDP Data: http://data.worldbank.org/indicator/NY.GDP.MKTP.KD.ZG Koester, Ulrich, Prospects for Grain Prices, University of Kiel Germany, siteresources.worldbank.org/ECAEXT/.../Prospects_Grain_Prices.ppt Westcott, Paul C., and Hoffman Linwood A., Price Determination for Corn and Wheat: The Role of Market Factors and Government Programs, http://usda.mannlib.cornell.edu/usda/ers/cornwheatprices/tb1878.pdf Chambers, William : Forecasting Feed Grain Prices in a Changing Environment, http://www.ers.usda.gov/publications/FDS/Jul04/fds04F01/fds04F01.pdf

http://www.nrcan.gc.ca/energy/publications/sources/crude/issues-prices/1329 http://physics.ucsc.edu/~drip/133/ch4.pdf

Appendix A

Review of AACE class 5 guidelines: CLASS 5 ESTIMATE (Typical level of project definition required: >0% to 2% of full project definition.) Class 5 estimates are generally prepared based on very limited information, and subsequently have wide accuracy ranges. As such, some companies and organizations have elected to determine that due to the inherent inaccuracies, such estimates cannot be classified in a conventional and systemic manner. Class 5 estimates, due to the requirements of end use, may be prepared within a very limited amount of time and with little effort expended. Class 5 estimates are prepared for any number of strategic business planning purposes, such as but not limited to market studies, assessment of initial viability, evaluation of alternate schemes, project screening, project location studies, evaluation of resource needs and budgeting, longrange capital planning, etc. (Source: AACE international)

Potash Price Data Review The data was provided through internal sources and appears to come from Green Markets. The data used for analysis dates from January 1990 to September of 2011. Figure A1 is a summary of the price data. Figure A2 shows the price data used for the analysis as well as the return data and a smoothed line for the return data. Figure A3 shows the LN of the return data. Similarly to Anselmo’s Oil data these data these data have the characteristics: 

Nearly symmetric distributions



fat tails-high kurtosis numbers



logistic distribution a better fit than lognormal

@RISK software was used to create a best fit model for the return data as well as the LN(return) data Figures 5 and 6 show these. The return data had log-logistic as the best fit with logistic second while the LN(return) data.

1990-01 1991-03 1992-05 1993-07 1994-09 1995-11 1997-01 1998-03 1999-05 2000-07 2001-09 2002-11 2004-01 2005-03 2006-05 2007-07 2008-09 2009-11 2011-01 1990-01 1990-10 1991-07 1992-04 1993-01 1993-10 1994-07 1995-04 1996-01 1996-10 1997-07 1998-04 1999-01 1999-10 2000-07 2001-04 2002-01 2002-10 2003-07 2004-04 2005-01 2005-10 2006-07 2007-04 2008-01 2008-10 2009-07 2010-04 2011-01

Potash Price Data

1000.0

900.0

800.0

700.0

600.0

500.0

400.0 Potash Price Data

300.0

200.0

100.0

0.0

Figure A1: Potash Price Data 1-1-1990 to 9-1-2011

1000 1.4

900

800 1.2

700 1

600

500

400

300

200

100

0 0.8 Price Data

0.6 Return data

0.4 Smoothed Return Data (10 pt moving average)

0.2

0

Figure A2: Price data and return data used in the analysis

1990-02 1991-01 1991-12 1992-11 1993-10 1994-09 1995-08 1996-07 1997-06 1998-05 1999-04 2000-03 2001-02 2002-01 2002-12 2003-11 2004-10 2005-09 2006-08 2007-07 2008-06 2009-05 2010-04 2011-03

LN Return Data

0.2

0.15

0.1

0.05 LN Return Data

0

-0.05

-0.1

-0.15

Figure A3: Ln of return data note the large jumps from 2006 to 2011

Figure A4-Best fit output from @RISK software for return data from Potash prices. The @Risk software indicated that the logistic distribution was the best fit, of the selected distributions, based on the Chi-sq test statistic being a minimum for this distribution (Palisade, 2011). We recognize that, according to the chi sq, our data are not well represented by the logistic but it still is the BEST option we have to perform the analysis.

Figure A5- Best fit output from @RISK software for LN of return data from Potash. The @Risk software indicated that the logistic distribution was the second best fit, of the selected distributions, based on the Chi-sq test statistic being a the second lowest for this distribution (Palisade, 2011). We recognize that, according to the chi sq, our data are not well represented by the logistic but it still is the BEST option we have to perform the analysis.

Appendix B

Risk level summary

Beta parameters used

max used (as a certainty 95% CI < min used (as a percentage of percentage of level 95% CI > mean mean alpha beta mean) mean) 1 39% 18% 1.5 30 82% 484% 2 25% 10% 2.64 19.5 83% 227% 3 10% 10% 2 2 87% 113% Table B1: Summary of beta distribution parameters used for Capital cost model. Distributions were created using @RISK software to get best fits for the desired percentage above and below the mean for a 95% Confidence interval. Capital Cost summary Level of Certainty Description Category Estimated Capital Cost about Estimate Labour Cost Site and utilities $ 7,651,678.00 2 Labour Cost Mine $ 58,773,590.00 1 Labour Cost Mill $ 6,473,565.00 1 Labour Cost Infrastructure Facilities $ 59,455.00 2 Labour Cost Off-site Facilities $ 5,156,163.00 2 Labour Cost Site Wide Indirects $ 17,899,872.00 1 Material Cost Site and utilities $ 7,793,937.00 3 Material Cost Mine $ 29,005,116.00 2 Material Cost Mill $ 4,835,906.00 3 Material Cost Infrastructure Facilities $ 135,000.00 1 Material Cost Off-site Facilities $ 4,335,350.00 1 Material Cost Site Wide Indirects $ 73,501,939.00 1 Construction equipment Cost Site and utilities $ 542,079.00 3 Construction equipment Cost Mine $ 727,338.00 3 Construction equipment Cost Mill $ 218,638.00 3 Construction equipment Cost Infrastructure Facilities $ Construction equipment Cost Off-site Facilities $ 19,800.00 3 Construction equipment Cost Site Wide Indirects $ 944,904.00 3 Mechanical Equipment Cost Site and utilities $ 224,306.00 3 Mechanical Equipment Cost Mine $ 68,146,627.00 2 Mechanical Equipment Cost Mill $ 4,960,137.00 3 Mechanical Equipment Cost Infrastructure Facilities $ 1,900,000.00 3 Mechanical Equipment Cost Off-site Facilities $ 3 Mechanical Equipment Cost Site Wide Indirects $ 3 Table B2: Summary of Capital costs and uncertainty levels used for Economic Analysis

Muriate Production Cost

y = 0.0642x - 2372.4 R² = 0.0713

Muriate Production Cost

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Linear (Muriate Production Cost)

Figure B1: Summary of Production cost/ton for Muriate product for Mosaic’s Carlsbad Operations, Note price spikes in October/November are due to scheduled yearly shutdowns

Appendix C

Table C1: Summary of supply/capability scenarios used for analysis Trial Parameters Mu Eta sigma High level of Oversupply 5 0.3 0.2 Oversupply 5.5 0.3 0.1 nominal supply/demand 6.1 0.3 0.3 tight supply/demand 6.5 0.5 0.4 Very tight supply/demand 7 0.1 0.5 Table C2: Summary of Mu and Eta parameters used for supply/demand scenarios