Question 5 of 6: Camm (1989) Parametric Shaft and Block-Caving Cost Models, Escalated to 2008

Question 5: Camm (1989) Parametric Shaft and Block-Caving Cost Models, Escalated to 2008 (20 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 component and total 1989 shaft capital/operating costs (5.1), the component and total 1989 block-caving mining capital/operating costs excluding the shaft (5.2), and the total shaft-plus-mining capital and operating costs escalated to 2008 (5.3), with commentary on model adequacy throughout.

Approach. Substitute X = 20,000 and D = 2,000 into every component formula of Table 5.1 (shaft) and Table 5.2 (block-caving mine) to get the 1989 component and "Total" line costs, cross-checking the sum of components against the independently regressed Total line each time; then multiply the 1989 shaft and mining totals by the ratio of the 2008 to 1989 capital and operating indices from Table 5.3.

1. Part 5.1 — shaft capital cost components, 1989. Each Table 5.1 capital term is evaluated at X=20,000, D=2,000 (Lumber, Fuel and Tires are marked "NAp" for a shaft and contribute nothing):

   Table 5.1 shaft capital cost, 1989 (USD)

   Category	Formula	Cost (USD)
   Labor	75D·X0.399	7,801,900
   Equipment	350X + 65D·X0.386	12,944,900
   Steel	25D·X0.373	2,010,300
   Lube	6D·X0.342	354,900
   Explosives	5D·X0.389	471,100
   Construction material	9D·X0.522	3,165,300
   Electricity	4D·X0.230	78,000
   Sum of components	—	26,826,400
   Total (Table 5.1 formula)	371X + 180D·X0.404	27,095,200

   Equipment (about 48% of the component sum) and Labor dominate, consistent with a mechanised shaft-sinking crew and a permanent hoisting/guide/service installation; the independently regressed "Total" formula comes out about 1% above the arithmetic sum of components, which is close enough to treat the model as internally consistent for a screening-level estimate.
2. Part 5.1 — shaft operating cost components, 1989.

   Table 5.1 shaft operating cost, 1989 (USD/short ton)

   Category	Formula	Cost (USD/st)
   Labor	2010/X	0.1005
   Equipment	0.325D/X	0.0325
   Steel	0.00014D	0.2800
   Lube	0.090D/X	0.0090
   Construction material	200/X	0.0100
   Electricity	0.0014D	2.8000
   Total (sum of the six printed components)	—	3.2320
   Cross-check: Camm's own regressed operating Total (not printed on this paper)	2343/X + 0.44D/X + 0.00163D	3.4212

   The operating-cost "Total" cell of Table 5.1 is left blank on this paper, so the shaft operating cost is the arithmetic sum of the six printed component terms, 3.232 USD/st; at 20,000 st/d × 365 d/yr this is an annual shaft operating cost of about USD 23.59 million. As a cross-check, Camm's own regressed Total line for the same table gives 3.421 USD/st (about USD 24.97 million/yr), about 6% higher — the same order of disagreement between a regressed total and the component sum seen for the capital lines. The Electricity term (2.80/st, over 80% of the operating total) is disproportionately large for what is normally a modest hoisting/pumping/ventilation power draw at a single shaft — worth flagging as a possible scaling artefact in the underlying regression (fitted mainly to shallower, lower-capacity shafts than this 2,000 ft, 20,000 st/d case) and sanity-checking against an independent kWh-based estimate before it is used in a real feasibility budget.
3. Part 5.2 — block-caving mining capital cost components, 1989 (excluding shaft). All ten Table 5.2 categories are pure functions of X alone (no depth term, since these are mining costs excluding the shaft):

   Table 5.2 block-caving mining capital cost, 1989 (USD)

   Category	Formula	Cost (USD)
   Labor	27,900X0.646	16,752,100
   Equipment	25,600X0.812	79,556,600
   Steel	4,410X0.685	3,896,200
   Lumber	149X0.902	1,129,100
   Fuel	10.6X0.897	76,400
   Lube	4.54X0.897	32,700
   Explosives	1,040X0.737	1,537,800
   Tires	1.87X0.946	21,900
   Construction material	31,100X0.591	10,831,000
   Electricity	50.4X0.748	83,100
   Sum of components	—	113,917,000
   Total (Table 5.2 formula)	64,800X0.759	119,139,800

   Equipment again dominates (about 70% of the component sum), consistent with the mechanised LHD/crusher/conveying fleet a block-caving operation of this scale requires; the Total-formula result runs about 4.6% above the component sum, a wider gap than the shaft model's — expected since the mining Total was regressed across a broad capacity range (4,000–40,000 st/d) rather than summed directly — and both figures should be carried forward with the difference treated as part of the estimate's inherent uncertainty band.
4. Part 5.2 — block-caving mining operating cost components, 1989 (excluding shaft).

   Table 5.2 block-caving mining operating cost, 1989 (USD/short ton)

   Category	Formula	Cost (USD/st)
   Labor	60.0X-0.305	2.9264
   Equipment	4.40X-0.230	0.4510
   Steel	0.217X0.0	0.2170
   Lumber	0.310X0.0	0.3100
   Fuel	0.894X-0.239	0.0838
   Lube	0.545X-0.253	0.0445
   Explosives	0.183X0.0	0.1830
   Tires	0.412X-0.151	0.0924
   Construction material	2.83X-0.182	0.4667
   Electricity	1.36X-0.060	0.7507
   Sum of components	—	5.5255
   Total (Table 5.2 formula)	48.4X-0.217	5.6432

   Labor is the single largest term (about 53% of the component sum), the pattern expected of an underground block-caving labour force; the negative exponent on every category reflects the economy of scale the model is built to represent (unit cost falls as capacity X rises), and a positive exponent here — giving a rising unit cost with capacity — would itself be a useful adequacy red flag, which none of the ten terms shows.
5. Part 5.3 — escalation factors, 1989→2008 (Table 5.3). $$\text{capital factor} = \dfrac{129.9}{95.5} = 1.3602, \qquad \text{operating factor} = \dfrac{141.9}{91.1} = 1.5576$$
6. Part 5.3 — total shaft and mining costs escalated to 2008. Applying the 2008 factors to the 1989 totals from Steps 1–4 (the printed "Total" lines, except shaft operating, where the table has no Total and the component sum is used):

   2008 escalated totals (USD)

   Item	1989	× factor	2008
   Shaft capital	27,095,200	1.3602	36,855,100
   Shaft operating (/st)	3.2320	1.5576	5.0343
   Mining capital	119,139,800	1.3602	162,055,000
   Mining operating (/st)	5.6432	1.5576	8.7899

   $$\boxed{C_{cap,2008} = 36.86\text{M} + 162.06\text{M} = 198.91\text{M USD}}$$ $$\boxed{c_{op,2008} = 5.034 + 8.790 = 13.82\ \text{USD/st}\ \ (\times 20{,}000 \times 365 \approx 100.9\text{M USD/yr})}$$ (Using Camm's regressed shaft operating Total of 3.421 USD/st instead would give 5.329 + 8.790 = 14.12 USD/st, about 103.1M USD/yr — within the uncertainty of a pre-feasibility estimate.)
7. Part 5.3 — adequacy of the 2008 estimate. A single scalar escalation factor applies the SAME multiplier to every cost category regardless of how that category's own inputs actually moved between 1989 and 2008 — a Labor-heavy line item and a Steel/Equipment-heavy line item (which tracked the 2000s commodity/construction boom far more steeply than site labour rates) did not escalate at the same rate in reality, so the blended-index result understates the true dispersion across categories even though the overall total is a reasonable order-of-magnitude figure. The estimate is further weakened by extrapolating a regression fitted to 1989 data forward nineteen years, and for the shaft model, by applying it at a capacity/depth combination near the edge of the sample the original Camm dataset was built from. Both models remain adequate for pre-feasibility/screening-level comparison between design options — exactly the use the question poses — but should never substitute for vendor-quote-based estimates once a project reaches a bankable feasibility study.