Question 17 of 29: 4.7: Net Smelter Return – Simplified Copper-Only Model

Question 4.4–4.7: Net Smelter Return – Simplified Copper-Only Model (10 marks)

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.

Find. The full mass-balance and value chain from mined ore through payable metal to the NSR expressed as $/mt of ore.

Approach. Work the mass balance forward from ore to concentrate (4.4), convert to a payable-metal basis per tonne of concentrate after the fixed unit deduction (4.5), net off treatment/transport/refining charges to get the net smelter value per tonne of concentrate (4.6), then convert back to a per-tonne-of-ORE basis via the concentrate:ore mass ratio to get the NSR (4.7).

1. 4.4.1–4.4.5 Ore-to-concentrate mass balance. $$\text{Metal in ore} = 275{,}000 \times 0.0232 = \boxed{6{,}380\text{ mt Cu}} \quad (4.4.1)$$ $$\text{Metal after mill recovery} = 6{,}380 \times 0.85 = \boxed{5{,}423\text{ mt Cu}} \quad (4.4.2)$$ $$\text{Concentrate tonnage} = \frac{5{,}423}{0.21} = \boxed{25{,}823.8\text{ mt concentrate/yr}} \quad (4.4.3)$$ Contained metal in concentrate (4.4.4) must equal the metal that entered it, 5,423 mt Cu – a useful mass-balance check: 25,823.8 × 0.21 = 5,423 mt ✓. In pounds (4.4.5): $$5{,}423 \times 2205 = \boxed{11{,}957{,}715\text{ lb Cu}\ (\approx 11.96\text{ million lb/yr})}$$
2. 4.5.1–4.5.5 Payable metal, per tonne of concentrate. Re-expressing on a per-mt-of-concentrate basis: metal per mt concentrate (4.5.2) = grade × 2205 lb/mt = 0.21 × 2205 = 463.05 lb Cu/mt conc. (this restates the contained metal of 4.5.1, 5,423 mt total, as an intensity). Metal per lb of concentrate (4.5.3) is simply the grade fraction itself, 0.21 lb Cu/lb conc. The fixed deduction (4.5.4): $$1.1\text{ units}\times 22.05\text{ lb/unit} = \boxed{24.255\text{ lb Cu/mt conc.}}$$ Payable metal (4.5.5): $$463.05 - 24.255 = \boxed{438.795\text{ lb payable Cu/mt conc.}}$$
3. 4.6.1–4.6.5 Charges, deductions and net value. Refining charge (4.6.2), levied on PAYABLE metal only: $$0.075 \times 438.795 = \boxed{\$32.91/\text{mt conc.}}$$ Total value of charges (4.6.1) – treatment + transport + refining: $$75 + 39 + 32.91 = \boxed{\$146.91/\text{mt conc.}}$$ Value of the unit deduction itself (4.6.3), i.e. the metal the mine is NOT paid for, valued at the copper price: $$24.255 \times 1.5 = \boxed{\$36.38/\text{mt conc.}}$$ Value after deductions and refining, i.e. the net smelter value (4.6.4) – gross contained-metal value minus the deduction value minus all charges: $$\underbrace{463.05\times1.5}_{\text{gross }\$694.58} - 36.38 - 146.91 = \boxed{\$511.28/\text{mt conc. (NSV)}}$$ (Equivalently and consistently: payable metal value minus TC, transport and refining: 438.795×1.5 − 75 − 39 − 32.91 = 658.19 − 146.91 = 511.28.) Converting to a per-tonne-of-ORE basis (4.6.5) via the concentrate:ore ratio (25,823.8 mt conc. / 275,000 mt ore = 0.09390): $$511.28 \times 0.09390 = \boxed{\$48.01/\text{mt ore}}$$
4. 4.7.1–4.7.3 NSR factor and NSR revenue. The NSR factor (4.7.1) benchmarks the realized ore value against the theoretical GROSS in-situ metal value (no recovery loss, no deductions/charges): gross in-situ value = 0.0232 × 2205 × 1.5 = $76.74/mt ore, so $$\text{NSR factor} = \frac{48.01}{76.74} = \boxed{0.626\ (\approx 62.6\%)}$$ – i.e. the mine realizes about 62.6% 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 (4.7.2) is the $48.01/mt ore figure carried forward from 4.6.5. The NSR expressed as $ revenue (4.7.3), applied to the full 275,000 mt/yr production: $$48.01 \times 275{,}000 = \boxed{\approx \$13.2\text{ million/year}}$$