24-MMP-A4 Mine Valuation and Mineral Resource Estimation · May 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-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 1.1–1.7); 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, volume–variance relations); Hustrulid, Kuchta & Martin, Open Pit Mine Planning and Design (mine valuation, NPV and cut-off grade methodology, mineable reserves, selective mining units); Gentry & O'Neil, Mine Investment Analysis (Canadian mining taxation, smelter/refining contract terms, net smelter return); SME Mining Engineering Handbook, 3rd ed. (mineral exploration and evaluation stages, ore reserve classification).
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.
Given.
| Quantity | Value |
|---|---|
| Annual net cash flow, R | 1,000 (CAD) per year, end-of-year |
| Duration, n | 4 years |
| Interest (discount) rate, i | 5% |
| Capital invested today | 3,500 (CAD) |
Find. The NPV of the 4-year annuity, and whether the investment is justified at 5%.
Approach. Discount the level end-of-year annuity with the standard uniform-series present-worth factor, then subtract the capital outlay to get NPV.
| Quantity | Value |
|---|---|
| Present-worth factor (P/A, 5%, 4) | 3.5460 |
| PV of cash-flow stream | CAD 3,545.95 |
| NPV | CAD 45.95 (positive – justified) |
Maximum-NPV cut-off grade categories. A maximum-NPV cut-off study evaluates, for every increment of grade in the reserve, the marginal effect on project NPV of processing that increment now versus later versus never, given the mill and mining capacity constraints (the Lane algorithm is the classical formalisation of this). Category 1 is material whose processing at the current point in the mine schedule maximizes overall project NPV – it clears the "opportunity-cost" cut-off that already accounts for the time value of deferring or advancing other ore, and is scheduled to the mill immediately. Category 2 is material below that opportunity-cost cut-off but still above the corporation's minimum acceptable return (its hurdle/required interest rate) if it were processed on its own – it is genuinely profitable, just not profitable enough to displace higher-value Category 1 material from today's limited mill capacity, so it should be set aside rather than discarded: mined now (since the marginal mining cost is already committed once the material is broken), but held back from immediate milling. Category 3 is material that is cash-flow positive at the moment of mining (revenue exceeds the marginal cost of processing it) but does not meet the corporate hurdle rate as a stand-alone decision – it should still be retained rather than sent to waste, because a positive cash flow, however small, is better than none, provided it does not itself displace higher-value material from mill capacity.
Selective stockpiling. Yes – Category 2 and 3 material should be placed in selective, grade-differentiated stockpiles close to the mill specifically so it can be reclaimed and processed once primary (higher-grade) mining is complete and the mill would otherwise be running out of feed, extending the mine's effective processing life at the lowest possible re-handling cost.
Valuing end-of-life stockpile reclaim as "ore". Stockpiled Category 2/3 material reclaimed at the END of mine life is the most heavily discounted material in the whole project – if primary mining runs 15–20 years, its present value at the outset can be a small fraction of its nominal value. It should nonetheless be included as "ore" in the feasibility study's reserve statement (with its correspondingly small, but non-zero, discounted NPV contribution) rather than omitted, both because it is a real, quantifiable and legally reportable mineral reserve under NI 43-101 economic-viability tests, and because omitting it understates total recoverable value and can distort early-life cut-off decisions that assume it will never be processed.
Destroyed value and a role for government. The maximum-NPV process, by construction, defers or entirely excludes lower-grade material whenever it would displace higher-NPV ore from finite mill capacity – from the corporation's own discounted-cash-flow perspective this is the value-maximizing choice, but from society's perspective it can permanently sterilize genuinely economic mineral resource (left in a final pit wall, or a stockpile never reclaimed if the mine closes early) that would have been profitably recoverable on its own. There is a legitimate role for government here, exercised through mine permitting and reclamation-plan conditions (e.g. requiring a documented, achievable stockpile-reclaim plan before mine closure is approved, or royalty/tax structures that do not penalize low-grade stockpile processing at the tail of mine life) to ensure that resources which are economic on a stand-alone basis, but simply "lose" the internal competition for mill capacity, are not abandoned in place once the corporation's own NPV-maximizing schedule has moved on.
