23-CS-1 Engineering Economics · May 2015
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — May 2015 — 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.
Initial $P=\$31{,}200$; salvage $S_n = 30{,}000(0.85)^{n}$; $EAC(n) = 31{,}200(A/P,10\%,n) - S_n(A/F,10\%,n) + [3{,}000 + 1{,}320(A/G,10\%,n)]$:
| n (yr) | Salvage | Capital cost | O&M equiv. | EAC(n) |
|---|---|---|---|---|
| 1 | $25,500 | $8,820 | $3,000 | $11,820 |
| 2 | $21,675 | $7,656 | $3,629 | $11,285 |
| 3 | $18,424 | $6,980 | $4,236 | $11,216 |
| 4 | $15,660 | $6,468 | $4,823 | $11,291 |
Capital cost falls with $n$ (the purchase price is recovered over more years) while the O&M equivalent rises (the $1,320/yr gradient accumulates), and the EAC is the sum of these two opposing trends.
EAC is minimized at n = 3 years (≈$11,216), so with constant costs and interest the furnace should be replaced every 3 years. The minimum is interior—EAC falls from year 1 to year 3 and rises again at year 4—so it is a genuine economic life and not simply the last year computed.
This is not the 15% rate used in part (a): the 15% declining-balance rate estimates the furnace's market scrap value, whereas 43.8% is the book depreciation rate that would write the asset down to $3,000 in four years. The two serve different purposes and need not agree.
A sunk cost is a cost already incurred that cannot be recovered. In replacement analysis it is irrelevant—only future costs and the asset's current market value affect the keep-or-replace decision. The original purchase price of an existing asset must be ignored; counting it leads to "throwing good money after bad."
