24-MMP-A4 Mine Valuation and Mineral Resource Estimation · December 2014
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, 2014-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 1.1–1.7); 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); Gentry & O'Neil, Mine Investment Analysis (Canadian mining taxation, smelter/refining contract terms, net smelter return); 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.
NPV method. Net Present Value discounts every year's after-tax free cash flow (revenue less operating cost, capital, and tax) back to the present at the company's cost of capital, and sums them: $$NPV=\sum_{t=0}^{n}\frac{CF_t}{(1+i)^t}$$ The mine plan, cut-off grade schedule and closure date that maximize NPV represent the "optimum" economic value of the asset under a given price/cost forecast. NPV is the accounting-familiar workhorse because it is additive across projects, directly comparable to a company's weighted-average cost of capital, and consistent with shareholder-wealth-maximization theory.
Related accounting-style measures. Internal Rate of Return (IRR, the discount rate at which NPV=0) and the payback period (years to recover initial capital, undiscounted or discounted) are commonly reported alongside NPV, though both have known weaknesses for mine valuation: IRR can be misleading with non-conventional cash-flow signs (e.g. large closure/reclamation outflows at the end of life) and payback ignores cash flows after the payback point, so it does not by itself value the mine's full working life.
Alternatives to NPV. Yes — several methods can capture value NPV alone misses. Real options valuation (using option-pricing techniques, e.g. binomial lattices or Black–Scholes-style models) explicitly prices the flexibility to expand, defer, contract or abandon the mine in response to future price/cost information — flexibility that static discounted-cash-flow NPV assumes away and which can be worth a substantial premium for a mine with optionality (e.g. a low-grade stockpile that is only processed if price rises). Decision-tree/Monte-Carlo simulation values a mine across a distribution of price and geological outcomes rather than a single deterministic case, better reflecting the risk profile actual investors face. Modern Asset Pricing (MAP), which discounts commodity-price-linked cash flows at the risk-free rate (using forward/futures curves for the price path) while discounting the remaining operating risk separately, is also used by some majors to avoid double-counting commodity price risk in a single blended discount rate. Each of these can produce a materially higher (and arguably more realistic) valuation than a conventional single-scenario DCF/NPV for an asset with genuine managerial flexibility.
