11-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.
Assumptions: present $t=0$ at end of 2015; construction $40M at ends of 2020–2023 ($t=5\text{–}8$); O&M from 2024 to 2063 ($t=9$ to $t=48$, 40 payments), first $3M growing 1%/yr; overhauls of $5M at operation years 10, 20, 30 ($t=18, 28, 38$; not at end of life); analysis horizon 48 years; $i=6\%$; no salvage.
$M
0 --+----+-----+---------+---------+---------+------+ (t=0..48)
t=5..8 t=9........................ t=48
-40(×4) O&M: 3.0 rising 1%/yr to t=48
↓ -5 ↓ -5 ↓ -5 (overhauls t=18,28,38)
Construction ($40M at $t=5\text{–}8$): $PW_c = 40(0.74726+0.70496+0.66506+0.62741)=40(2.74469)=\$109.79$M.
O&M (geometric, $A_1=3$M, $g=1\%$, $n=40$): the closed form values the series one period before its first payment, i.e. at $t=8$, so $P_8 = 3\frac{1-(1.01/1.06)^{40}}{0.05}=3(17.10499)=\$51.3150$M; then $PW_{OM}=51.3150(P/F,6\%,8)=51.3150(0.62741)=\$32.20$M.
Overhauls ($5M at $t=18,28,38$): $PW_{oh}=5(0.35034+0.19563+0.10924)=5(0.65521)=\$3.28$M.
The expressway costs an equivalent of about $9.28M per year over the analysis horizon (again counting only costs, not the value of improved traffic flow).