Question 1 of 11

Question 1.1 (6 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.

1.1.1 — the O’Hara cost-estimating formula. O’Hara’s method is a parametric (order-of-magnitude, ±30–40%) capital- or operating-cost model of the power-law form Cost = A·T^b, where T is a single dominant capacity parameter — almost always daily or annual mill/mine throughput — and A and b are empirical constants fitted to a database of real, built mine costs of the same general type (open pit vs. underground, mill type, mining method). The exponent b is normally well below 1.0 (commonly 0.6–0.8), capturing the economy-of-scale effect: doubling throughput less than doubles cost, because fixed items (administration buildings, access roads, the crusher foundation) do not scale linearly with tonnage. O’Hara derived A and b the way every parametric cost model is built: he assembled a data set of actual, recently-built mines/mills of a given category, plotted ln(Cost) against ln(T) for each, and fitted a straight line by least squares — the fitted slope is b and the fitted intercept, exponentiated, is A. Because A is calibrated against actual reported costs at the time those mines were built, A is only valid for that base year and must be escalated (1.1.2) before use.

1.1.2 — updating to present-day dollars. A cost estimate anchored to a base year is escalated to the estimate date using a published cost index ratio: Cost _present = Cost _base × (Index _present / Index _base), using a SEPARATE index for capital items and for operating items since they escalate at different rates (labour vs. steel/equipment vs. energy). O’Hara-family cost studies are conventionally updated using (1) the Marshall & Swift Equipment Cost Index (or its mining-specific derivative, the Mining and Milling Cost Index historically published in the Engineering and Mining Journal), and (2) the Canadian Mining Journal annual cost-index review / CIM Bulletin cost-update papers that continued the O’Hara series (e.g. Camm 1991, USBM IC 9298 and the Mular & Poulin CIM Special Volume 47 update). A separate capital-index and operating-index pair must be applied because construction-labour and steel prices historically outpace consumables and power costs.