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23-CS-1 Engineering Economics · December 2019

Question 5 of 5: Laser Cutter — Remaining Economic Life

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Notes on this paper

National Exams — December 2019 — 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 follow.

Question 5: Laser Cutter — Remaining Economic Life (25 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.

(a) EAC of Keeping the Old Machine n More Years (i = 10%)

Keeping the defender $n$ more years forgoes its current market value $MV_0 = \$49{,}000$ today and recovers the salvage $S_n$ at year $n$. Its EAC is the capital-recovery cost plus the annual equivalent of the O&M costs actually incurred in years $1\ldots n$:

$$EAC(n) = \underbrace{(MV_0 - S_n)(A/P,10\%,n) + S_n(0.10)}_{\text{capital cost}} + \underbrace{\Big[\textstyle\sum_{k=1}^{n} OM_k (P/F,10\%,k)\Big](A/P,10\%,n)}_{\text{O\&M equivalent}}$$

Factors used: $(P/F,10\%,k) = 0.909091,\ 0.826446,\ 0.751315,\ 0.683013$ for $k=1\ldots4$ and $(A/P,10\%,n) = 1.10,\ 0.576190,\ 0.402115,\ 0.315471$ for $n=1\ldots4$.

Worked row, $n=2$: capital cost $=(49{,}000-19{,}875)(0.576190)+19{,}875(0.10)=16{,}781.5+1{,}987.5=\$18{,}769$; O&M present worth $=17{,}000(0.909091)+21{,}320(0.826446)=\$33{,}074.4$, so O&M equivalent $=33{,}074.4(0.576190)=\$19{,}057$; $EAC(2)=18{,}769+19{,}057=\$37{,}826$. The other rows follow identically (O&M present worths $15,454.5, $53,214.1 and $76,282.2 for $n=1, 3, 4$):

n (yr)Capital costO&M equiv.EAC(n)
1$22,400$17,000$39,400
2$18,769$19,057$37,826
3$14,974$21,398$36,372
4$14,005$24,065$38,070

(b) Remaining Economic Life

EAC is minimized at n = 3 years (≈$36,372), so the old cutter's remaining economic life is 3 years.

(c) Replace Now?

The new machine's EAC ($35,000) is below the old machine's minimum EAC ($36,372) and below its next-year marginal cost ($39,400). Since the challenger is cheaper than keeping the defender, yes—replace the old machine now.

(d) Sunk Cost

The original $130,000 purchase price (7 years ago) is the sunk cost—unrecoverable and irrelevant. Only the current market value ($49,000) and future costs matter.

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