11-CS-1 Engineering Economics · May 2014
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — May 2014 — 11-CS-1 Engineering Economics. Open book; non-communicating calculator permitted. Any four of the five questions constitute a complete paper; all questions are of equal value. Fully worked solutions to all five questions follow; standard compound-interest factors are used and minor rounding is immaterial.
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.
A sunk cost is a cost already incurred that cannot be recovered by any future decision. In a replacement analysis, sunk costs are irrelevant—the original purchase price of an existing asset does not affect the keep-or-replace decision; only future costs and the asset's current market value matter. Including sunk costs leads to the error of "throwing good money after bad."
Initial cost $P=\$5{,}200$ (compressor + running-in); salvage $S_n = 5{,}000(0.85)^{n}$; $EAC(n) = P(A/P,10\%,n) - S_n(A/F,10\%,n) + [500 + 220(A/G,10\%,n)]$:
| n (yr) | Salvage $S_n$ | Capital cost | O&M equiv. | EAC(n) |
|---|---|---|---|---|
| 1 | $4,250 | $1,470 | $500 | $1,970 |
| 2 | $3,613 | $1,276 | $605 | $1,881 |
| 3 | $3,071 | $1,163 | $706 | $1,869 |
| 4 | $2,610 | $1,078 | $804 | $1,882 |
Two modelling points are worth stating explicitly, as the exam's own instructions invite. First, the $200 running-in cost is incurred immediately and is not recoverable, so it is added to the first cost ($P = \$5{,}200$) but is not part of the declining-balance base — salvage is estimated on the $5,000 purchase price alone. Second, the $220 escalation is a uniform arithmetic gradient, so it is converted with $(A/G,10\%,n)$ rather than the geometric factor; note that $(A/G,10\%,1)=0$, which is why year 1's O&M equivalent is exactly the base $500.
The EAC is minimized at n = 3 years (EAC ≈ $1,869), so with constant costs and interest the compressor should be replaced every 3 years—its economic life.
