24-MMP-A4 Mine Valuation and Mineral Resource Estimation · May 2017
Question 18 of 18: Net Smelter Return – Simplified Copper-Only Model
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Notes on this paper
EGBC National Exam — Mining and Mineral Processing Engineering, 09-MMP-A4 Mine Valuation and Mineral Resource Estimation, 2017-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 1.1–1.6); 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 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, transportation logistics); SME Mining Engineering Handbook, 3rd ed. (cost-estimating relationships, mineral exploration/evaluation stages, ore reserve classification); Evans, An Introduction to Ore Geology and Guilbert & Park, The Geology of Ore Deposits (ore deposit models); CIM Best Practice Guidelines and NI 43-101 (Canadian Securities Administrators).
Question 6.4: Net Smelter Return – Simplified Copper-Only Model (9 marks)
Find. The full mass-balance and value chain from mined ore through payable metal to the NSR expressed as $/mt of ore, on the basis of the mine's 1,000 mt/day ore production.
Check
The question states the mine produces ore only 5 days/week while the mill runs 7 days/week continuously – this describes a mine/mill throughput mismatch requiring an ore stockpile buffer, but every quantity requested below (6.4.1–6.4.4) is defined on a PER-1,000-MT-OF-ORE basis, which converts directly and consistently to a per-day figure regardless of which day of the week that tonne was mined or milled. The mine/mill schedule detail therefore does not change any of the boxed results below; it is flagged here as a modelling assumption rather than silently ignored.
Fig. 6.4 – Mass and value chain: ore → mill (85% recovery) → 21%-Cu concentrate → smelter deductions/charges → net smelter value (per tonne concentrate) → NSR (per tonne ore), all on a 1,000 mt/day ore basis.
Approach. Work the mass balance forward from ore to concentrate (6.4.1), convert to a payable-metal basis per tonne of concentrate after the fixed unit deduction (6.4.2), net off treatment/transport/refining charges to get the net smelter value per tonne of concentrate (6.4.3), then convert back to a per-tonne-of-ORE basis via the concentrate:ore mass ratio to get the NSR (6.4.4).
6.4.1.1–6.4.1.5 Ore-to-concentrate mass balance. $$\text{Metal in ore} = 1{,}000 \times 0.025 = \boxed{25.0\text{ mt Cu/day}} \quad (6.4.1.1)$$ $$\text{Metal after mill recovery} = 25.0 \times 0.85 = \boxed{21.25\text{ mt Cu/day}} \quad (6.4.1.2)$$ $$\text{Concentrate tonnage} = \frac{21.25}{0.21} = \boxed{101.19\text{ mt concentrate/day}} \quad (6.4.1.3)$$ Contained metal in concentrate (6.4.1.4) must equal the metal that entered it, 21.25 mt Cu – a useful mass-balance check: 101.19 × 0.21 = 21.25 mt ✓. In pounds (6.4.1.5): $$21.25 \times 2205 = \boxed{46{,}856.25\text{ lb Cu/day}}$$
6.4.2.1–6.4.2.5 Payable metal, per tonne of concentrate. Re-expressing on a per-mt-of-concentrate basis: contained metal in concentrate (6.4.2.1) restates 6.4.1.4 as an intensity, i.e. the concentrate's own 21% grade. Metal per mt concentrate (6.4.2.2) = grade × 2205 lb/mt = 0.21 × 2205 = 463.05 lb Cu/mt conc. Metal per lb of concentrate (6.4.2.3) is simply the grade fraction itself, 0.21 lb Cu/lb conc. The fixed deduction (6.4.2.4): $$1.1\text{ units}\times 22.05\text{ lb/unit} = \boxed{24.255\text{ lb Cu/mt conc.}}$$ Payable metal (6.4.2.5): $$463.05 - 24.255 = \boxed{438.795\text{ lb payable Cu/mt conc.}}$$
6.4.3.1–6.4.3.5 Charges, deductions and net value. Refining charge (6.4.3.1), levied on PAYABLE metal only: $$0.1 \times 438.795 = \boxed{\$43.88/\text{mt conc.}}$$ Total value of charges (6.4.3.2) – treatment + transport + refining: $$100 + 50 + 43.88 = \boxed{\$193.88/\text{mt conc.}}$$ Value of the unit deduction itself (6.4.3.3), i.e. the metal the mine is NOT paid for, valued at the copper price: $$24.255 \times 2.2 = \boxed{\$53.36/\text{mt conc.}}$$ Value after deductions and refining, i.e. the net smelter value (6.4.3.4) – gross contained-metal value minus the deduction value minus all charges: $$\underbrace{463.05\times2.2}_{\text{gross }\$1{,}018.71} - 53.36 - 193.88 = \boxed{\$771.47/\text{mt conc. (NSV)}}$$ (Equivalently and consistently: payable metal value minus TC, transport and refining: 438.795×2.2 − 100 − 50 − 43.88 = 965.35 − 193.88 = 771.47.) Converting to a per-tonne-of-ORE basis (6.4.3.5) via the concentrate:ore ratio (101.19 mt conc. / 1,000 mt ore = 0.10119): $$771.47 \times 0.10119 = \boxed{\$78.07/\text{mt ore}}$$
6.4.4.1–6.4.4.3 NSR factor and NSR revenue. The NSR factor (6.4.4.1) benchmarks the realized ore value against the theoretical GROSS in-situ metal value (no recovery loss, no deductions/charges): gross in-situ value = 0.025 × 2205 × 2.2 = $121.28/mt ore, so $$\text{NSR factor} = \frac{78.07}{121.28} = \boxed{0.644\ (\approx 64.4\%)}$$ – i.e. the mine realizes about 64.4% of the ore's theoretical in-situ copper value once mill recovery, the smelter deduction, and treatment/transport/refining charges are all accounted for. The value per mt of ore (6.4.4.2) is the $78.07/mt ore figure carried forward from 6.4.3.5. The NSR expressed as $ revenue (6.4.4.3), applied to the mine's full 1,000 mt/day ore production: $$78.07 \times 1{,}000 = \boxed{\approx \$78{,}065/\text{day}}$$
