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UBC Theses and Dissertations

Financial optimization of mining plant size McIntosh, Douglas Grant


The hypothesis of this study is that the optimal plant size for a mining venture is dependent upon both uncontrollable and controllable variables. Examples of variables which are uncontrollable to the firm are characteristics of the orebody, capital and product markets, projected price levels, and tax structure. Controllable variables in determining plant size are rate of recovery, level of recovery, capital costs, and operating costs. The primary purpose of this study is to delineate the effects of these variables, both singly and jointly, upon plant size and to present a model which will interrelate the variables with that scale of plant which will maximize the value of the firm. A secondary purpose of the study is to compare the impact of both Canadian and United States tax laws upon the profitability of a given operation, and upon the optimal grade-capacity combination to be employed for a given orebody. The difference of the impact of Canadian and United States tax laws with respect to the conservation of resources is also considered. After each of the controllable and uncontrollable variables is defined and analysed, a detailed analysis is made of various methods of mine valuation, with the objective being to identify the valuation method which most closely relates to the value of the firm. Then a model is constructed which will give the mine-life annual cash flows for a given orebody under various concentrator-capacity--cut-off-grade combinations. These cash flows are then converted to internal rates of return and benefit-to-cost ratios, which are contoured for various cut-off grades and concentrator capacities under various metal prices. The model assumes an orebody with a tonnage of 40e ⁽²ˉ ⁵x⁾ million tons, where x is the cut-off grade, in percent copper. Contour plots of benefit-to-cost ratio and internal rate of return were constructed for cut-off grades ranging from 0% to 1% copper, and for concentrator capacities ranging from 5000 tons-per-day to 50,000 tons-per-day, at net smelter returns of 40¢ per lb. to per 46¢ per lb. of contained copper. The tax system under which the highest profits are attained is Canadian tax laws with pre-1968 British Columbia taxes. The operation is least profitable under United States tax laws. However, optimal plant size is least sensitive to changes in metal price under United States tax laws, and most sensitive to price changes under Canadian tax laws with pre-1968 British Columbia taxes. Similarly, optimal cut-off grade is most insensitive to changes in metal price under Canadian tax laws with pre-1968 British Columbia taxes, and most sensitive to product price changes under United States tax laws. Therefore, it can be shown that under United States tax laws, the response of an operation to changing product prices would be to change the optimal cut-off grade, while in Canada, particularly under pre-1968 British Columbia taxes, the response would be to change the optimal operating capacity. Therefore, American tax laws provide the greatest flexibility for responding to changes in product price. The tax system which produces the greatest degree of conservation of resources, as is reflected by completeness of ultimate extraction, is the American case. The lowest extraction level would result under Canadian taxes, with pre-1968 British Columbia/taxes.

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