24-MMP-A4 Mine Valuation and Mineral Resource Estimation · December 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-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 1.1–1.8); 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, anisotropy); Hustrulid, Kuchta & Martin, Open Pit Mine Planning and Design (mine valuation, NPV/IRR and cut-off grade methodology); Gentry & O'Neil, Mine Investment Analysis (smelter/refining contract terms, net smelter return, taxation and risk); Guilbert & Park, The Geology of Ore Deposits, and Evans, Ore Geology and Industrial Minerals (VMS/SEDEX and porphyry deposit models); SME Mining Engineering Handbook, 3rd ed. (mineral exploration/evaluation stages, ore reserve classification); 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.
O'Hara's method (CIM Bulletin, 1980) regresses historical mine cost data against operating capacity (and, for underground mines, depth) in a single power-law form applied consistently to every cost component and to the total: $C = a\,X^{b}$ (surface/capital, per-tonne or total-dollar terms), sometimes extended to $C=a\,X^{b}D^{c}$ where $X$ is daily/annual throughput and $D$ is depth, with the coefficients $a,b,c$ fitted separately for each cost category (mine capital, mill capital, mine operating cost per tonne, mill operating cost per tonne, and so on) from a database of built mines. Because every component shares the same functional form, a preliminary capital or operating estimate for a NEW deposit of a given size can be produced quickly at scoping/PEA level simply by evaluating each category's own $a,X^b$ term and summing, escalated from the regression's base year to the estimate date by the appropriate capital or operating cost index.
O'Hara's companion mine-life rule (the same empirical relationship widely published as Taylor's rule) ties economic mine life to the size of the RESERVE: life (years) ≈ 0.2 × (expected reserve tonnage)0.25, equivalently a daily mining rate of roughly (reserve tonnes)0.75/70 at about 350 operating days per year. Life therefore grows only as the fourth root of reserve size, so larger deposits are mined at a proportionally faster rate and each year deplete a SMALLER fraction of their reserve only slowly — e.g. a 100 Mt reserve gives 0.2 × (108)0.25 = 20 years (about 14,300 t/d), while a 1 Mt reserve gives about 6.3 years. Different textbook editions quote slightly different fitted constants, so the rule is best treated as a quick sizing/reasonableness check on a proposed mining rate against reserve tonnage, not a precise design number.
Compared against discounted-cash-flow (time-value-of-money) studies, the O'Hara rule is only an approximate reasonableness check: it says nothing about discount rate, cash-flow timing/front-loading, or metal price assumptions, so two mines with the same O'Hara-implied life can have very different NPVs if one front-loads high-grade ore. In practice O'Hara's rule is used at the conceptual stage to bound a sensible mining rate range; the rate that actually maximizes NPV is then found by running full discounted cash flow sensitivities across a range of throughputs, which frequently favours a somewhat FASTER mining rate (shorter life) than the O'Hara heuristic alone would suggest, because pulling cash flow forward is rewarded by discounting even though it raises peak capital intensity.
