18-Geol-B8 Resource Economics & Valuation · May 2016
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — May 2016 — 04-Geol-B8, Resource Economics and Valuation. Three-hour, open-book exam; any non-communicating calculator permitted. Six questions are printed; the exam's own cover notes state that only the first four questions in the answer book are marked, and each of the six is of equal value (25 marks) — all six are answered here as a complete study resource. Most questions require mathematical solutions, and clarity and organization of the steps involved are explicitly graded.
Reference texts: Torries, Evaluating Mineral Projects: Applications and Misconceptions (SME, 1998) — discounted cash flow valuation of mine projects, net smelter return economics, royalty valuation, and cut-off grade theory; Rudenno, The Mining Valuation Handbook, 4th ed. (Wrightbooks, 2012) — comparable-transaction and appraised-value (Kilburn) methods, copper-equivalent grade, and resource/reserve-stage valuation; EGBC Geoscience Professional Practice Guidelines for assumption-disclosure conventions on open-book calculations.
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.
Cut-off grade is the minimum grade at which a block of mineralized material can be extracted, processed and sold at a net positive economic value under the prevailing costs, prices, recoveries and metallurgical terms; material above the cut-off is classified as ore and scheduled for mining, while material below it is treated as waste. A distinction that matters throughout the rest of this question is between a marginal (breakeven) cut-off — the grade at which incremental revenue exactly equals the incremental cost of mining and processing that increment of material, generally used to decide whether ore already brought to surface should be sent to the mill or to the waste dump — and an internal or optimizing cut-off, which additionally accounts for opportunity cost (mill capacity is a scarce, shared resource) and is typically set higher than the marginal cut-off to maximize the project's net present value rather than simply its total tonnage.
Every mineral deposit has a grade-tonnage relationship: as the cut-off grade is raised, progressively less of the deposit qualifies as ore (tonnage falls), but the material that remains is, by construction, higher grade on average (quality rises), since the lowest-grade blocks are the first to be excluded. Lowering the cut-off has the opposite effect — more tonnage qualifies as ore and mine life may extend, but the average grade of that reserve is diluted downward, which can reduce total contained-metal recovery per tonne processed and, if pushed too far, can turn marginally profitable material into a net loss once processing and general/administrative costs are properly allocated. Because tonnage and grade move in opposite directions with cut-off, there is generally an optimum cut-off (the internal cut-off of part (i)) that maximizes NPV rather than simply maximizing either tonnage or grade in isolation.
Exploration-stage projects and producing mining projects use cut-off grade very differently. An exploration-stage project has no mine plan, no committed capital and no fixed mill capacity yet, so cut-off grade is applied only conceptually — typically a simple marginal/breakeven estimate based on preliminary, often generic cost and price assumptions — purely to decide which drill intersections and blocks are reasonable to report as a mineral resource at all; the resulting resource estimate carries wide uncertainty and is not yet a statement of what will actually be mined. A producing mine, by contrast, actively manages a live, frequently recalculated internal cut-off grade as an operating and scheduling tool: it directly controls pit or stope design, short- and long-range production scheduling, and the ore/waste designation applied to material as it is actually mined, and it is revisited whenever metal prices, costs, recoveries or remaining mill capacity change materially. In short, cut-off grade is a conceptual reporting threshold at the exploration stage and an actively managed operating and value-optimization lever at the production stage.
Individual assay values in a sample database occasionally include extreme outliers — from the true nugget effect of coarse gold or similar minerals, from sampling or sample-preparation error, or from a genuinely anomalous local enrichment — that are not representative of the surrounding block of ground. Because grade estimation (compositing, then interpolation or kriging) spreads each sample's influence over a search neighbourhood, a single uncapped extreme value can disproportionately bias the estimated average grade of a much larger volume of ground than the sample itself represents, inflating both the estimated tonnage above cut-off and the estimated average grade of that tonnage. Capping (top-cutting) sets a statistically-derived ceiling on individual assay values — commonly identified from a histogram, a decile/probability-plot analysis of the population, or a target coefficient of variation — before compositing and interpolation, so that no single extreme sample can dominate the local estimate. The practical implication of getting this wrong is a reserve statement that looks better on paper than the deposit will actually deliver: when mining catches up to an uncapped, overstated estimate, the mined grade reconciles below the predicted grade, undermining both the mine plan and the confidence of investors and lenders in the resource model — which is exactly why capping methodology is a standard, disclosed part of any competent-person resource estimate under the applicable reporting codes.
