NivaarExam PrepOfficial exam papers ↗

23-CS-1 Engineering Economics · May 2015

Question 1 of 5: Expressway — Present and Annual Worth

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

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 1: Expressway — Present and Annual Worth (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.

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.

(a) Cash-Flow Diagram

05101520253035404548t (yr)construction 40M/yr, t=5–8 (2020–2023)O&M: 3.0M at t=9, rising 1%/yr to 4.42M at t=48 (40 payments, to end 2063)overhaul 5M at t=18, 28, 38 (offset right of the O&M arrow)All flows are costs ($M, downward); t=0 = end of 2015; no salvage.
Figure Q1(a): cash-flow diagram, present (end of 2015, t=0) to end of 2063 (t=48). Arrow lengths are to scale; the O&M arrows grow 1%/yr.

(b) Present Worth (t = 0, i = 6%)

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.

$$PW = -(109.79 + 32.20 + 3.28) \approx \boxed{-\$145.3\text{M}}$$

(c) Annual Worth (over the 48-year horizon)

$$AW = PW\,(A/P,6\%,48) = -145.3(0.063898) \approx \boxed{-\$9.28\text{M/yr}}$$

The expressway costs an equivalent of about $9.28M per year over the analysis horizon (counting only costs—the value of the improved traffic flow is not part of this calculation).

← Paper overview