24-MMP-A4 Mine Valuation and Mineral Resource Estimation · May 2018
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, 2018-May. 3 hours duration; closed book, with one handwritten 8.5×11 in. reference sheet (both sides) permitted; only an approved Sharp or Casio calculator allowed. Question 1 is compulsory (40 marks, parts 1.1–1.9); 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); Hustrulid, Kuchta & Martin, Open Pit Mine Planning and Design (mine valuation, cut-off grade theory, incremental analysis); Gentry & O'Neil, Mine Investment Analysis (Canadian mining taxation, cash flow/risk, smelter contract terms, NSV/NSR); SME Mining Engineering Handbook, 3rd ed. (ore deposit models, mineral exploration/evaluation stages, equipment utilization); O'Hara, T.A., “Quick Guides to the Evaluation of Orebodies,” CIM Bulletin, Feb. 1980 (parametric capital-cost estimating); CIM Definition Standards for Mineral Resources and Mineral Reserves / National Instrument 43-101 (resource/reserve classification and reporting).
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 O'Hara formulation. O'Hara's method fits a power-law regression to a cross-section of real operating mines: each capital or operating cost COMPONENT (mine development, mill, tailings, infrastructure…) is expressed as $$C_i = K_i \cdot X^{n_i}$$ where X is mine/mill throughput capacity (and for some components, depth D enters as a second power-law factor), Ki is a fitted constant, and the exponent ni (typically well below 1, often 0.6–0.85) captures the economy of scale for that component — larger operations cost more in total but LESS per tonne of capacity. Every component and the total cost use the SAME functional form, only the fitted K and n differ, which is what makes the method quick to apply from a one-page set of coefficients rather than a full engineering estimate.
The mine-life rule. The companion rule of thumb (widely taught alongside O'Hara's cost curves and generally attributed in the literature to H.K. Taylor) estimates an economically optimal mine life directly from the tonnage of the reserve: $$\text{Life (years)} \approx 0.2 \times (\text{Reserve tonnes})^{0.25}$$ i.e. mine life scales with the FOURTH ROOT of tonnage, so a mine must be roughly sixteen times larger to double its optimum life. The rule is a useful first-pass sanity check on a proposed production rate (it flags an obviously undersized or oversized mill relative to the reserve) but it is a poor tool once the time value of money enters a feasibility study: it is derived purely from the STATIC tonnage/rate relationship observed across many operating mines and says nothing about discounting. A faster production rate that shortens mine life below the rule's suggestion can still be NPV-superior if it pulls cash flow forward into earlier, less-discounted years, and conversely a rule-compliant slower rate can destroy value if it merely defers cash flow without a compensating grade or recovery benefit. The rule is therefore a reasonable STARTING point for capacity sizing, never a substitute for an explicit DCF sensitivity on throughput rate.
