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.
Net cash flow, R. The actual cash received or paid by the project in a given period – revenue less operating costs, capital expenditure, taxes and royalties actually paid – a real dollar movement, not an accounting profit figure (it excludes non-cash items such as depreciation/CCA, which only affect R indirectly through the tax it shields).
Discount rate, r. The annual rate used to convert a future cash flow into today's equivalent value, reflecting the time value of money and the risk of the project; for a mining project r is typically the company's weighted-average cost of capital adjusted upward for country/commodity/technical risk (a mining discount rate commonly runs 5–12% real).
Duration (time) of cash flow, t. The number of periods (years) from the valuation date (t = 0) to the period in which a given net cash flow R occurs; it is the exponent applied to the discount factor and is measured consistently with the compounding period of r (annual r → annual t).
Present value or worth, PV. The value today of a single future cash flow R occurring at time t, PV = R/(1+r)t; more generally the value today of any stream of cash flows once each has been individually discounted back to t = 0.
Net present value (or worth), NPV. The sum of the present values of every net cash flow in the project's life – inflows and outflows – including the initial capital outlay: NPV = Σ Rt/(1+r)t. A positive NPV means the project returns more than the discount rate demands; NPV is the standard go/no-go and project-ranking criterion in mine valuation.
Effect of NPV analysis on reclamation costs. Reclamation and closure costs occur at the very end of mine life, often 10–30+ years after the valuation date, so discounting shrinks them to a small fraction of their nominal (undiscounted) amount – a $50 million closure liability discounted 20 years at 8% is worth only about $10.7 million today. This is a well-known criticism of relying on NPV alone for closure planning: it can understate the true environmental liability and create an incentive to under-provide for reclamation, which is exactly why Canadian jurisdictions require security (reclamation bonds/trusts) sized on the nominal closure cost estimate rather than its discounted present value.
