Question 2 of 6: Capital and Operating Cost Estimation

Question 2: Capital and Operating Cost Estimation (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.

2.1 — Cost estimation methods and Hugh Taylor's rule

2.1.1 Cost estimation methods. A cost estimation method is a systematic, repeatable procedure for predicting a project's capital and/or operating cost before it is actually built, ranging from a rough order-of-magnitude estimate based on a single scaling parameter (capacity, tonnage — the "six-tenths rule" family, including the parametric O'Hara/Mular&Poulin formulas used below) through a factored/parametric estimate built up from major cost centres, to a detailed (definitive) estimate priced from completed engineering, quantity take-offs and vendor quotes. Each level trades estimating effort and time against accuracy, matching the AACE Class 5 (order-of-magnitude, ±30–50%) through Class 1 (definitive, ±3–10%) framework used across the mining and process industries.

2.1.2 Hugh Taylor's rule. Hugh Taylor's rule is a well-known mining-industry rule of thumb linking a project's economic mining rate (and hence much of its capital scale) to the size and depth of the orebody itself — commonly expressed as mine life in years being roughly proportional to the fourth root of the reserve tonnage (or, in its production-rate form, daily/annual mining rate scaling with a fractional power of total reserve tonnes), so that a bigger orebody supports a proportionately larger, but not linearly larger, production rate and mine life. It is used at the very earliest stage of overall cost estimation to set a defensible target production rate (and hence the capacity variable T that every downstream capital-cost formula, including all of Question 2.3, is built around) directly from an orebody's tonnage, before any detailed mine design exists to derive that rate a more rigorous way.

2.2 — Escalating 1980 and 1998 costs to 2019

As a capital cost estimator today I would not apply a general inflation index (CPI) to a mining capital cost, because construction and mining-equipment costs have historically escalated at a different rate than consumer prices. Instead I would apply a mining/milling-specific cost index ratio, escalating each historical figure independently to 2019 dollars: $$C_{2019} = C_{1980}\times\dfrac{\text{Index}_{2019}}{\text{Index}_{1980}} \qquad\text{and}\qquad C_{2019} = C_{1998}\times\dfrac{\text{Index}_{2019}}{\text{Index}_{1998}}$$ using the Marshall & Swift Mining/Milling index (or, equivalently, the historical USBM/Camm capital-cost index family the O'Hara/Mular&Poulin formulas themselves are built from), reading the index value published for each of the three years from the current M&S M/M index tables and applying the ratio directly — exactly as Question 1.5.2 describes and exactly the operation used to keep the Question 2.3 formulas (originally published against a 1980s/1990s base year) valid for a present-day (2019) capital estimate. Because the two source years (1980, 1998) sit on different points of the same index series, each must be escalated with its own year-specific ratio — a single blended "18 years vs. 39 years" average factor would systematically mis-price whichever of the two costs is estimated less directly.

2.3 — Parametric fixed-capital cost estimate (T = 1500 t/day ore, W = 10 m)

Given. Ore-only hoisting rate $T = 1500$ t/day; stope width $W = 10$ m; the O'Hara/Mular&Poulin parametric cost formulas quoted above for compressed-air plant ($C_1$), mine development ($C_2$), underground mining equipment ($C_5$) and the underground maintenance facility ($C_6$).

Find. $Q$, $C_1$ (2.3.1); $C_2$, $C_5$, $C_6$ (2.3.2); the total fixed cost excluding milling and $C_3,C_4,C_7$–$C_{10}$ (2.3.3); and a reliability comment (2.3.4).

Approach. Substitute $T$ and $W$ directly into each independent power-law formula, then sum the computed cost centres for the 2.3.3 total.

1. Part 2.3.1 — compressed-air quantity and compressor plant cost. $$Q = 0.0957\times T^{0.16} = 0.0957\times1500^{0.16} = 0.0957\times3.222 = \boxed{0.308\ \text{m}^3/\text{s}}$$ Then $$C_{11} = 369{,}938\times Q^{0.8} = 369{,}938\times0.308^{0.8} = \$144{,}300\qquad C_{12} = 81{,}382\times Q^{0.7} = 81{,}382\times0.308^{0.7} = \$35{,}700$$ $$\boxed{C_1 = C_{11}+C_{12} = \$180{,}100}$$ A quantity of $Q\approx0.3\ \text{m}^3/\text{s}$ (about 650 cfm) is a modest, realistic single-header compressed-air demand for a mid-size mine at this tonnage — well within the range a single reciprocating or rotary-screw compressor plant covers, so $C_1$ is a plausible order-of-magnitude estimate for that plant, though it prices only the compressor package itself and not the underground distribution piping, which can add materially to the true installed cost.
2. Part 2.3.2 — development, equipment and maintenance-facility costs. $$C_2 = 37{,}033\times T\times W^{-0.8} = 37{,}033\times1500\times10^{-0.8} = 37{,}033\times1500\times0.1585 = \boxed{\$8{,}804{,}000}$$ $$C_5 = 27{,}963\times W^{-0.3}\times T^{0.8} = 27{,}963\times10^{-0.3}\times1500^{0.8} = 27{,}963\times0.5012\times347.5 = \boxed{\$4{,}869{,}200}$$ $$C_6 = 31{,}915\times T^{0.5} = 31{,}915\times\sqrt{1500} = 31{,}915\times38.73 = \boxed{\$1{,}236{,}100}$$ Both $C_2$ and $C_5$ fall with a WIDER stope ($W^{-0.8}$ and $W^{-0.3}$) — a wider stope needs proportionately less development metreage and equipment per tonne hoisted, which is the physically expected trend.
3. Part 2.3.3 — total fixed cost (compressor + development + equipment + maintenance facility only). Summing the four cost centres actually computed above, and excluding milling/processing and the location-dependent items $C_3$ (power/water/services), $C_4$ (access/townsite) and $C_7$–$C_{10}$ (surface plant, feasibility, supervision/camp, administration) as the question specifies: $$C_{\text{fixed}} = C_1+C_2+C_5+C_6 = 180{,}100+8{,}804{,}000+4{,}869{,}200+1{,}236{,}100 = \boxed{\$15{,}089{,}400}$$

2.3.4 — Reliability and applicability of this methodology. These O'Hara/Mular&Poulin-style formulas are single-variable power-law regressions fitted to a historical database of built mines, so they are reliable for a fast, defensible order-of-magnitude (Class 4/5, roughly ±25–35%) screening estimate early in a project's evaluation — exactly the "quick fix" role identified in Question 1.5.4 — and they scale sensibly across a wide range of T and W, correctly capturing the direction (if not the exact magnitude) of economies of scale. Their applicability is limited, however, because: they were regressed against mines built in a specific era and jurisdiction, so unusual geology, remote-site logistics, extreme depth or a mining method outside the database's population can fall well outside the fitted relationship's valid range; they use only T and W as inputs, ignoring genuinely cost-driving factors such as rock competence (support cost), depth (haulage/ventilation cost) and labour-market conditions; and because escalating a decades-old regression via a single blended cost index (Question 2.2) compounds the base regression's uncertainty with the index's own approximation error. The methodology is therefore appropriate for screening/ranking alternative mine plans and for an early feasibility check, but a project actually proceeding to construction requires a detailed, engineered estimate before capital is committed.