Preliminary fixed capital cost and capacity-expansion cost: 24-MMP-B5 Mineral Processing Design and Operations, May 2016, Q5

Question 5: Preliminary fixed capital cost and capacity-expansion cost (5/6)

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. Equipment cost ratio table above (factor $F_1$ and current purchased cost per category). Future capacity ratio $1.30$; M&S escalation ratio $1.25$ over the same 5-year horizon.

Find. (a) Preliminary total fixed capital cost. (b) Preliminary cost of the facility at the expanded capacity, in future (escalated) dollars.

Approach. The equipment-cost-ratio (factored/Lang-type) method installs each equipment category by multiplying its own purchased cost by its own factor, then sums across categories; the six-tenths rule then rescales the whole facility to the new capacity and re-escalates by the M&S index ratio.

Installed cost per category. $\text{Installed}_i = F_{1,i}\times\text{Cost}_i$: $$\begin{aligned} \text{Crushers} &= 3.5\times2{,}500{,}000 = \$8{,}750{,}000 \\ \text{Electric motors} &= 8.5\times700{,}000 = \$5{,}950{,}000 \\ \text{Conveyors} &= 2.3\times500{,}000 = \$1{,}150{,}000 \\ \text{Dust collectors} &= 3.5\times1{,}000{,}000 = \$3{,}500{,}000 \\ \text{Screens} &= 2.3\times120{,}000 = \$276{,}000 \\ \text{Instrumentation} &= 4.1\times850{,}000 = \$3{,}485{,}000 \\ \text{Non-specified equip.} &= 3.0\times750{,}000 = \$2{,}250{,}000 \end{aligned}$$
Sum for total fixed capital. $$\text{Fixed capital} = \boxed{\$25{,}361{,}000}$$
Six-tenths-rule scale-up for the 30% capacity increase. $$\text{Cost}_2 = \text{Cost}_1\left(\frac{\text{Capacity}_2}{\text{Capacity}_1}\right)^{0.6}=25{,}361{,}000\times(1.30)^{0.6}=25{,}361{,}000\times1.1705=\$29{,}686{,}000$$
Escalate to future dollars via the M&S index. $$\text{Cost}_2^{\text{escalated}} = 29{,}686{,}000\times1.25=\boxed{\$37{,}106{,}000}$$ For reference, escalating the ORIGINAL (unexpanded) facility by the same M&S ratio alone gives $25{,}361{,}000\times1.25=\$31{,}701{,}000$; the incremental cost attributable purely to the 30% capacity increase is therefore $37{,}106{,}000-31{,}701{,}000\approx\$5{,}405{,}000$.

Final Results — Question 5
Quantity	Value
Preliminary fixed capital cost (present)	USD 25,361,000
Facility cost at expanded (130%) capacity, future dollars	USD 37,106,000
Incremental cost of the capacity increase alone	≈ USD 5,405,000

Topic: Factored (equipment-cost-ratio) capital estimation and six-tenths-rule capacity scaling.

Key relations: $\text{Installed cost}=\sum F_{1,i}\text{Cost}_i$; six-tenths rule $\text{Cost}_2=\text{Cost}_1(Q_2/Q_1)^{0.6}$; M&S escalation is linear in the index ratio.

Why this works: Installation, piping, instrumentation and indirect costs scale roughly proportionally with a piece of equipment's own purchase price (captured in each category's own factor), while total plant capital scales sub-linearly with capacity (economies of scale) because many fixed costs — engineering, site works, some structural steel — don't grow one-for-one with throughput, which is exactly what the 0.6 exponent captures.

Common pitfall: Applying the M&S escalation before the six-tenths capacity scaling changes nothing here (both are multiplicative), but forgetting to apply BOTH factors — scaling for capacity while leaving costs at the present-day M&S index, or vice-versa — understates the true future cost.

Source: Mular & Poulin, CIM Special Volume 47 (1998); SME Mining Engineering Handbook, 3rd ed., capital cost estimation chapter.

Question 5 of 8: Preliminary fixed capital cost and capacity-expansion cost

Question 5: Preliminary fixed capital cost and capacity-expansion cost (5/6)