Component and Total Mining Costs at 50,000 t/day: 24-MMP-A4 Mine Valuation and Mineral Resource Estimation, May 2017, Q11

Question 3.2: Component and Total Mining Costs at 50,000 t/day (15 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.

Component	Cost-per-day formula ($, T in t/d)
Drilling	2.85 T^0.7
Blasting	4.76 T^0.7
Loading	4.01 T^0.7
Haulage	27.10 T^0.6
General	9.98 T^0.7
Daily tonnage, T	50,000 t/day (ore + waste)

Find. Cost per day and per tonne, for each component and in total, at T=50,000 t/day.

Approach. Evaluate T^0.7 and T^0.6 once at T=50,000, apply each component's own K, sum for the daily total, then divide every daily figure by T to get the per-tonne figures.

Scale factors. $$T^{0.7}=50{,}000^{0.7}=1{,}947.3 \qquad T^{0.6}=50{,}000^{0.6}=662.6$$
Individual component costs, per day and per tonne. $$\text{Drilling} = 2.85\times1{,}947.3=\boxed{\$5{,}547.84/\text{day}}\ \big(\div T = \$0.1110/\text{t}\big)$$ $$\text{Blasting} = 4.76\times1{,}947.3=\boxed{\$9{,}265.86/\text{day}}\ \big(\div T = \$0.1853/\text{t}\big)$$ $$\text{Loading} = 4.01\times1{,}947.3=\boxed{\$7{,}805.91/\text{day}}\ \big(\div T = \$0.1561/\text{t}\big)$$ $$\text{Haulage} = 27.10\times662.6=\boxed{\$17{,}879.33/\text{day}}\ \big(\div T = \$0.3576/\text{t}\big)$$ $$\text{General} = 9.98\times1{,}947.3=\boxed{\$19{,}427.17/\text{day}}\ \big(\div T = \$0.3885/\text{t}\big)$$
Total cost, per day and per tonne. Summing all five components: $$\text{Total/day} = 5{,}547.84+9{,}265.86+7{,}805.91+17{,}879.33+19{,}427.17=\boxed{\$59{,}926.11/\text{day}}$$ $$\text{Total/tonne} = \frac{59{,}926.11}{50{,}000}=\boxed{\$1.1985/\text{tonne}\ (\approx\$1.20/\text{t})}$$

Component	$/day	$/tonne
Drilling	5,547.84	0.1110
Blasting	9,265.86	0.1853
Loading	7,805.91	0.1561
Haulage	17,879.33	0.3576
General	19,427.17	0.3885
Total	59,926.11	1.1985 (≈$1.20)

Comment on automating feasibility studies with these formulae (part b). Because every component here shares the SAME general power-law form and the per-tonne figures (Column 3 above) are exactly the answer to part (b)'s "what would you expect these costs per tonne to be" – Haulage and General dominate the per-tonne total (0.358 and 0.389 $/t respectively, together ≈62% of the $1.20/t total), with Loading, Blasting and Drilling contributing the remainder. This structure is attractive for AUTOMATING early-stage (scoping/PEA) cost estimation in a spreadsheet or software tool: given only a candidate daily tonnage T, every cost line is generated instantly with no detailed equipment-list engineering, allowing rapid screening of many scale/site scenarios and quick sensitivity analysis on throughput. However, this convenience comes with real limitations that a feasibility-level study cannot accept: the K, x coefficients are historical regression averages that embed an implicit "typical" strip ratio, haul distance, rock hardness and labour cost structure that may not match the specific project; the formulae give NO breakdown into fixed vs. variable cost (needed for break-even and downside-scenario analysis) or capital vs. operating cost; and because the coefficients are tied to a specific historical cost-index base year, they must be escalated correctly (a step easy to omit when the model is "automated" and treated as a black box). Automating with these formulae is therefore appropriate for rapid PRE-feasibility screening across many scenarios, but must be replaced by first-principles, site-specific estimating once a project is carried to bankable feasibility.

Concept & Theory

Topic: Parametric (power-law) open-pit mining cost estimation.

Key relations: Component cost/day = K·T^x; component cost/tonne = K·T^x−1; total = Σ over components.

Why this works: Summing independently-fitted power-law terms (each capturing one activity's own scale-economy exponent) is more flexible than a single blended power-law for the whole mine, since drilling/blasting/loading/general (x=0.7) and haulage (x=0.6, a stronger economy of scale reflecting fixed haul-fleet dispatch/maintenance overhead spread over more tonnes) genuinely behave differently with scale.

Common pitfall: Reporting only the total cost/tonne without checking which component dominates – here Haulage and General together are ~62% of unit cost, so a scale change or haul-profile change affects the total far more than an equivalent change in Drilling.

Source: Camm, T.W. (1991), USBM IC 9298; Hustrulid, Kuchta & Martin, Ch. 4.

Question 11 of 18: Component and Total Mining Costs at 50,000 t/day

Question 3.2: Component and Total Mining Costs at 50,000 t/day (15 marks)