24-MMP-A4 Mine Valuation and Mineral Resource Estimation · May 2017
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
EGBC National Exam — Mining and Mineral Processing Engineering, 09-MMP-A4 Mine Valuation and Mineral Resource Estimation, 2017-May. 3 hours duration; one handwritten 8.5×11 in reference sheet permitted (not an open-book exam); only approved Sharp or Casio calculators allowed. Question 1 is compulsory (40 marks, parts 1.1–1.6); candidates then select THREE of the five optional Questions 2–6 (20 marks each) to complete the paper.
Reference texts: Isaaks & Srivastava, An Introduction to Applied Geostatistics (variogram modelling, kriging estimators, volume–variance relations); Hustrulid, Kuchta & Martin, Open Pit Mine Planning and Design (mine valuation, NPV and cut-off grade methodology, mineable reserves); Gentry & O'Neil, Mine Investment Analysis (Canadian mining taxation, smelter/refining contract terms, net smelter return, transportation logistics); SME Mining Engineering Handbook, 3rd ed. (cost-estimating relationships, mineral exploration/evaluation stages, ore reserve classification); Evans, An Introduction to Ore Geology and Guilbert & Park, The Geology of Ore Deposits (ore deposit models); CIM Best Practice Guidelines and NI 43-101 (Canadian Securities Administrators).
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
The algebra is correct: dividing the total daily cost C=KTx by the daily tonnage T gives the unit (per-tonne) cost c=C/T=KTx−1=KT−(1−x)=K/T(1−x), exactly as claimed – this is simple algebraic rearrangement, not a new empirical claim. The economically meaningful content is in the exponent x: whenever x<1 (the typical case for essentially every mining cost category – drilling, blasting, loading, haulage, general/overhead), unit cost DECLINES as scale T increases, which is the mathematical statement of economies of scale in mining – fixed/semi-fixed cost components (supervision, mobile-equipment capital recovery, fleet dispatch overhead) are spread over more tonnes as throughput rises. The smaller the exponent x, the stronger this scale effect (Haulage's x=0.6 below shows the strongest economy-of-scale response of the five components, since a 0.6 power grows total cost more slowly, relative to T, than a 0.7 power does).
These power-law (Taylor's Law / cost-capacity) relationships are empirically FITTED to historical mine cost data across many operations at different scales, not derived from first-principles engineering – K and x are regression coefficients specific to a mining method, region and cost-index base year, and must be escalated (via a capital/operating cost index ratio) before use at a later date. They are valuable for FAST, early-stage (scoping/PEA-level, ±30–50%) screening of many candidate scales or sites, but should not be substituted for a detailed, first-principles equipment/labour estimate at feasibility level, since the fitted curve represents an INDUSTRY AVERAGE relationship that may not reflect a specific site's actual geology, strip ratio, haul profile, labour market or equipment fleet.
