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11-CS-1 Engineering Economics · December 2019

Question 2 of 5: University Football Stadium — Present and Future Worth

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

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 2: University Football Stadium — Present and Future 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.

Note on the question. The construction in Question 2 starts in 2024 (not in 2021) and runs for four years at $10M per year.

Timeline ($t=0$ = end of 2019, so $t = \text{year} - 2019$): construction $10M at $t=5\text{–}8$ (the four years 2024–2027); O&M geometric, first $2M at $t=9$ (2028, the first year after completion) growing 1%/yr for 45 payments to $t=53$ (2072); overhaul $8M at $t=30$ (2049); salvage $+15M at $t=53$; $i=6\%$.

(a) Cash-Flow Diagram

Cash flows in millions of dollars; present (t = 0) = end of 2019.2019t = 02024t = 52029t = 102039t = 202049t = 302059t = 402072t = 534 × 10 M/yr construction (t = 5–8)O&M: 2 M at t = 9, rising 1%/yr to t = 538 M overhaul (t = 30)+15 M salvage (t = 53)

Figure 1 — Cash-flow diagram for the stadium, present (t = 0) at the end of 2019. Downward arrows are costs, the upward arrow at t = 53 is the salvage receipt. The O&M series (gold) begins at t = 9 and grows 1% per year.

(b) Present Worth (i = 6%)

Construction ($10M at $t=5\text{–}8$): $PW_c = 10(0.747258+0.704961+0.665057+0.627412) = 10(2.744688) = \$27.45$M.

O&M (geometric, $g=1\%$, $n=45$ payments at $t=9\ldots53$, so the series has its present value at $t=8$): $2\dfrac{1-(1.01/1.06)^{45}}{0.06-0.01}=2(17.7263)=35.45$M; to $t=0$: $35.45(P/F,6\%,8)=35.45(0.627412)=\$22.24$M.

Overhaul: $8(P/F,6\%,30)=8(0.174110)=\$1.39$M. Salvage: $15(P/F,6\%,53)=15(0.045582)=\$0.68$M. Combining:

$$PW = -27.45 - 22.24 - 1.39 + 0.68 \approx \boxed{-\$50.40\text{M}}$$

(c) Future Worth (t = 53, end of 2072)

$$FW = PW\,(F/P,6\%,53) = -50.40(21.9387) \approx \boxed{-\$1{,}106\text{M}}$$

With no revenue modelled, the worth is negative; the −$50.40M present cost is what the university weighs against the capacity and reputational benefits of the new stadium. Note how sensitive the answer is to the start date: had construction begun in 2021 instead of 2024, the same four $10M outlays would sit three years nearer the present and the present worth would be about $10M worse, at −$60.35M.