Question 11 of 11: Mine Cost Centres, Cost/Inflation Indexes, and Parametric Capital Cost

Question 6: Mine Cost Centres, Cost/Inflation Indexes, and Parametric Capital Cost (20 marks, optional)

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.

6.1 – Major cost items by centre. Drilling (blast-holes, excl. explosives) is typically dominated by: drill bits/rock-bit consumption ($\approx$30%), fuel/energy ($\approx$25%), labour/wages and benefits ($\approx$25%), and maintenance/major-component wear parts ($\approx$20% – the mirror image of the Pareto ranking already worked through in Question 1.6.1 for this same cost centre). Truck haulage: tyres ($\approx$30%, historically the single largest swing item on large rigid-frame haul trucks), fuel ($\approx$25%), labour ($\approx$20%), and maintenance/major-component rebuilds (engine, transmission, final drive, $\approx$25%). Shovel loading: GET (ground-engaging tools – dipper teeth, lip, adapters, $\approx$25%), labour ($\approx$25%), maintenance/major-component rebuild (swing, hoist, crowd, hydraulics, $\approx$30%), and power/fuel ($\approx$20%). These percentages are illustrative industry-typical splits (exact figures vary by mine and equipment class); the pedagogical point, per Question 1.6, is that 2–3 of these four items usually account for the bulk of the sector's cost.

6.2 – Cost index vs. inflation index. A cost index is a dimensionless ratio (base year $=100$) tracking how the PRICE of a specific, defined basket of mining capital goods or services (e.g. mill equipment, earthmoving equipment, construction labour) has moved over time relative to that base year – it is used to escalate a parametric capital-cost estimate (Question 1.1.3's O'Hara/Camm method, applied numerically in 6.3–6.4) from the estimate's base year to today. An inflation index (e.g. a national Consumer Price Index or GDP deflator) tracks the general purchasing power of currency across the WHOLE economy, not any specific capital-goods basket. Two commonly used capital-cost indexes in mining practice: the Marshall & Swift Equipment Cost Index (mining/milling machinery-weighted) and the CE (Chemical Engineering) Plant Cost Index or an equivalent mining-specific capital-cost index (e.g. the Camm/CIM capital and operating indexes referenced in Question 1.1.3). The problem with applying ONE blended index to every mine cost sector is that labour-heavy sectors (open-pit mining labour, for instance) and equipment/steel-heavy sectors (drills, shovels, trucks – Question 6.3) do not inflate at the same annual rate; a single index systematically over- or under-states one or the other. Using the SEPARATE capital-equipment and general-inflation indexes together IMPROVES the 6.1 cost-index estimates by escalating each of the four major cost items (drill bits, tyres, GET, labour, etc.) with the index that actually tracks its own market (equipment/consumable items with the equipment cost index, labour/wage items with a labour or general inflation index), rather than escalating the sector's whole cost with one number.

Given. Power-law cost-capacity relations $P=aX^b$ (1997 US dollars) for each equipment class; unit conversions $1\text{ kg}=2.20462\text{ lb}$, $1\text{ m}^3=1.30795\text{ yd}^3$, $1\text{ tonne}=1.10231$ short tons; equipment sizes 55,000 kg pull-down drill, 53 m³ shovel bucket, 300 tonne truck.

Find. The 1997 capital cost of each machine, then the 2015 cost after the given inflation factor.

Approach. Convert each machine's size to the units the regression was fitted in ($X$ in lb, yd³, or short tons as specified), evaluate $P=aX^b$, then apply the single stated inflation factor to escalate 1997→2015.

1. 6.3.1 – Drill (55,000 kg pull-down, converted to lb). $$X=55{,}000\times2.20462=121{,}254\text{ lb}$$ $$P=400\times X^{0.67}=400\times121{,}254^{0.67}=\boxed{\$1{,}018{,}900\text{ (1997)}}$$
2. 6.3.2 – Shovel (53 m³ bucket, converted to yd³). $$X=53\times1.30795=69.3\text{ yd}^3$$ $$P=540{,}000\times X^{0.75}=540{,}000\times69.3^{0.75}=\boxed{\$12{,}973{,}000\text{ (1997)}}$$
3. 6.3.3 – Truck (300 tonne, converted to short tons). $$X=300\times1.10231=330.7\text{ short tons}$$ $$P=20{,}000\times X^{0.90}=20{,}000\times330.7^{0.90}=\boxed{\$3{,}703{,}000\text{ (1997)}}$$

6.4 – Escalation to 2015 and realism check. Applying the given factor (1997 $1 = 2015 $2.00): $$\text{Drill: }\$1.02\text{M}\times2.00=\boxed{\$2.04\text{M}}\qquad\text{Shovel: }\$12.97\text{M}\times2.00=\boxed{\$25.95\text{M}}\qquad\text{Truck: }\$3.70\text{M}\times2.00=\boxed{\$7.40\text{M}}$$ The drill and truck figures are broadly in the right neighbourhood of real 2015 large rotary-drill and 300-tonne-class rigid-frame haul-truck prices. The shovel figure is NOT realistic – a real 2015-vintage electric mining shovel with a 53 m³ (roughly 69 yd³) dipper, among the very largest shovels ever built, typically cost on the order of US$15–20M, not $26M, and this bucket size sits well beyond the range of shovels the original 1997 regression was almost certainly fitted against (most mining shovels of that era carried buckets well under 30 yd³). This is a textbook case of extrapolating a power-law regression outside its calibration range: the fitted exponent ($b=0.75$) captures the AVERAGE economy-of-scale relationship across the machines actually sampled, but a single blended 2.00× inflation factor also ignores that (i) equipment-specific technology and design changes (not captured by a generic inflation index) have materially changed shovel manufacturing cost since 1997, (ii) a simple two-variable power law cannot capture step-changes in cost at the very largest equipment sizes (specialised transport, site-erection cranes, and limited-competition supply at the top of the size range all add cost non-linearly), and (iii) currency/exchange-rate movements between 1997 and 2015 are folded into one US-dollar inflation number that may not match the equipment's true country-of-manufacture cost base. The drill and truck sizes here sit much closer to the historical middle of their respective regressions, which is exactly why THEIR extrapolated 2015 figures read as more plausible.