Question 19 of 19: 6.5: NSV and NSR Calculation for a Copper Concentrate

Question 6.3–6.5: NSV and NSR Calculation for a Copper Concentrate (12 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. Concentrate grade $M=28\%$ Cu; unit deduction $D=1$ (grade point); exchange rate $\text{fx}=1.25$ C$/US$; metal price $P=\text{US}\$3.00$/lb; refining charge $R=\text{US}\$0.30$/lb; treatment charge $T=\text{US}\$100.00$/DMT; precious-metal credits $C=\text{US}\$40.00$/DMT; 1 DMT $=2204.62$ lb. (Head grade 0.2% and concentrator recovery 90% establish that the mine must process roughly $28/(0.2\times0.9)\approx156$ tonnes of ore per tonne of concentrate produced — not needed for the per-tonne-of-concentrate NSV/NSR figures asked for here, but the link back to per-tonne-of-ore economics if required.)

Find. NSV (6.3) and NSR as a % (6.4) per DMT of concentrate, and the mine-level NSR after transport (6.5).

Approach. Convert the payable (grade-deduction-adjusted) copper content of one DMT of concentrate to payable pounds, value it at the metal price for NSV, then net off refining, treatment and credits for NSR, express as a % of the gross contained value, and finally deduct wet-tonne transport cost for the mine-level NSR.

1. Payable copper content per DMT of concentrate. The unit deduction removes 1 percentage point of grade before any metal is deemed payable: $$\text{Payable Cu} = \frac{M-D}{100}\times 2204.62 = \frac{28-1}{100}\times2204.62$$ $$\boxed{\text{Payable Cu} = 595.25\ \text{lb/DMT concentrate}}$$
2. NSV (6.3) — gross payable value before refining/treatment. $$NSV_{\text{US\$}} = 595.25 \times 3.00 = \text{US}\$1{,}785.75/\text{DMT}$$ $$NSV_{\text{C\$}} = 1{,}785.75\times1.25$$ $$\boxed{NSV \approx C\$2{,}232.18/\text{DMT concentrate}}$$
3. NSR (6.4) — net of refining, treatment, plus credits. $$\text{Refining} = 595.25\times0.30 = \text{US}\$178.58$$ $$NSR_{\text{US\$}} = 1{,}785.75 - 178.58 - 100.00 + 40.00 = \text{US}\$1{,}547.17/\text{DMT}$$ $$NSR_{\text{C\$}} = 1{,}547.17\times1.25 \approx C\$1{,}933.96/\text{DMT}$$ Expressed as a % of the gross contained-metal value (full 28% grade, no deduction, at metal price, currency cancels in the ratio): $$\text{Gross value} = \frac{28}{100}\times2204.62\times3.00 = \text{US}\$1{,}851.88/\text{DMT}$$ $$NSR\% = \frac{1{,}547.17}{1{,}851.88}\times100$$ $$\boxed{NSR \approx 83.5\%\ \text{of gross contained value}}$$
4. Mine-level NSR after transport (6.5) — account for 7% moisture and CDN$125.00/WMT freight. A concentrate that is 7% water by weight means 1 DMT corresponds to more than 1 wet tonne, since the wet tonne includes the water: $$1\ \text{WMT} = (1-0.07)\ \text{DMT} \;\Rightarrow\; 1\ \text{DMT} = \frac{1}{1-0.07} = 1.0753\ \text{WMT}$$ $$\text{Transport cost} = 125.00\times1.0753 \approx C\$134.41/\text{DMT}$$ $$NSR_{\text{mine, C\$}} = 1{,}933.96 - 134.41$$ $$\boxed{NSR_{\text{mine}} \approx C\$1{,}799.55/\text{DMT concentrate} \;(\approx77.7\%\ \text{of gross value})}$$