24-MMP-A4 Mine Valuation and Mineral Resource Estimation · December 2013
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, 2013-Dec. 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 1.1–1.7); candidates then select FOUR of the six optional Questions 2–7 (15 marks each) to complete the paper.
Reference texts: Isaaks & Srivastava, An Introduction to Applied Geostatistics (variogram modelling, kriging estimators, compositing and support); Hustrulid, Kuchta & Martin, Open Pit Mine Planning and Design (NPV/cut-off grade methodology, cost estimating, financing structures); Torries, Evaluating Mineral Projects: Applications and Misconceptions (SME) (mine valuation, cost of capital, inflation treatment); Gentry & O'Neil, Mine Investment Analysis (net smelter return, smelter/refining contract terms); SME Mining Engineering Handbook, 3rd ed. (mineral economics, capital and operating cost estimating).
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.
What Taylor's Rule states. Taylor's Rule (H.K. Taylor, 1977 – often called the "fourth-root rule") is an empirical relationship between a deposit's total mineable reserve tonnage and the optimum mine life (and, by extension, the optimum production rate). In its most common form, mine life in years is approximated as Life ≈ 0.2×(Reserve tonnes)0.25, so the optimum daily/annual production rate follows simply as reserve tonnage divided by that life. Applied at the scoping/pre-feasibility stage, it lets an engineer sanity-check a proposed production rate against the historical pattern of how large mines of comparable tonnage have actually been developed, well before a detailed capital/operating cost model or discounted cash-flow schedule exists.
Scientific basis. The rule has no basis in first-principles engineering optimization – it is not derived from marginal-cost/marginal-revenue analysis, from an NPV-maximizing production-rate model, or from any physical law. It is a purely empirical regression: Taylor fitted the fourth-root relationship to a historical database of dozens of operating mines' actual reserve tonnage versus actual mine life, and the observed correlation held reasonably well across a wide range of deposit sizes and commodities. Its "scientific" content is therefore statistical (an observed central tendency across many independently optimized projects, each of which presumably did approximate an economic optimum for its own site-specific costs, grades and prices) rather than theoretical. Because of this, the rule is best treated as an order-of-magnitude reasonableness check – useful for flagging a production-rate assumption that is wildly inconsistent with industry practice – and not as a substitute for a site-specific NPV-optimized production-rate study. Later authors (e.g. Long, 2009) have re-fitted the coefficient against more recent mine populations, confirming the functional FORM is durable while the fitted constant drifts with era and commodity mix.
