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11-CS-1 Engineering Economics · May 2017

Question 4 of 5: Gasoline versus All-Electric Car

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

Notes on this paper

National Exams — May 2017 — 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 4: Gasoline versus All-Electric Car (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.

Annual Energy Costs

Gasoline: $20{,}000\times\frac{6.5}{100}\times0.85 = \$1{,}105$/yr. Electric: $20{,}000\times\frac{12}{100}\times0.14 = \$336$/yr. Electric saves $769/yr. Resale after $n$ years: value $\times(0.9)^n$.

(a) Net Cost After 3 Years

$$\text{Gasoline} = 24{,}000(1-0.729) + 1{,}105(3) = 6{,}504 + 3{,}315 = \$9{,}819$$
$$\text{Electric} = 36{,}000(1-0.729) + 336(3) = 9{,}756 + 1{,}008 = \$10{,}764$$

The gasoline car is more economic after 3 years ($9,819 < $10,764), by $945. The reason is visible in the two components: three years of energy saving is only $3(769)=\$2{,}307$, while the electric car's extra $12,000 of purchase price sheds $12{,}000(0.271)=\$3{,}252$ of market value over the same three years. At 0% interest the comparison is simply depreciation plus running cost, so the premium has to be recovered out of fuel savings alone.

(b) Gas Price to Justify the Electric Over 4 Years

Only the difference between the two cars matters, so work with the $12,000 price premium directly. Over four years that premium loses $12{,}000(1-0.9^{4})=12{,}000(0.3439)=\$4{,}127$ of value, which is the extra net cost the electric car must recover. The commuter burns $20{,}000\times\frac{6.5}{100}=1{,}300$ L/yr, so at a gas price $p$ the yearly saving is $1{,}300p-336$. Setting the four years of saving equal to the extra cost:

$$4(1{,}300p - 336) = 4{,}127 \;\Rightarrow\; 5{,}200p = 5{,}471 \;\Rightarrow\; p \approx \boxed{\$1.05/\text{L}}$$

(c) Years to Justify the Electric

The electric saves $769/yr; extra net cost $12{,}000(1-0.9^{n})$. Justified when $769n \ge 12{,}000(1-0.9^{n})$. Testing brackets the break-even between $n=10$ ($7{,}690 < 7{,}816$) and $n=11$ ($8{,}459 > 8{,}234$); solving $769n = 12{,}000(1-0.9^{n})$ gives $n\approx\boxed{10.37\ \text{years}}$. The electric is justified only for roughly 10.4 years of ownership or more.