Methods for calculating the minimum amortization tonnage and maximum present value for an ore body

The discussion is divided into three parts. Part I describes a procedure for determining the mining rate that gives the minimum amortization tonnage required of an ore body, and the amount of that tonnage. The basic idea is that amortization tonnage is equivalent to the estimated capital costs, including interest, divided by the estimated operating profit per ton. Both capital costs and operating profit per ton can be expressed as functions of mining rate by making use of empirical equations. Therefore, amortization tonnage can be expressed as a function of mining rate. The amortization tonnage is calculated for a series of mining rates, one of which will indicate a minimum tonnage. Part II describes a procedure for calculating the optimum mining rate to obtain maximum present value of an ore body, when mining rate is the only variable. An expression is derived which gives present value in terms of mining rate, and this expression is solved using various rates. The results are plotted, and the resulting graph will reveal a maximum present value at one mining rate. Part III shows how optimum operating conditions for maximum present value can be determined when mining method, mining sequence, milling method, cut-off, and mining rate are variable. The procedure consists essentially of calculating the present value for all practical combinations of the above variables, and selecting the combination that gives the highest present value. If desired, cut-off can be eliminated as one of the variables by making it equivalent to the operating and capital cost of mining a ton of ore --Abstract, page 7