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23-CS-1 Engineering Economics · December 2019

Question 4 of 5: Gasoline versus All-Electric Car

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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 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: Gas $=20{,}000\times\tfrac{6.5}{100}\times0.85=\$1{,}105$/yr; Electric $=20{,}000\times\tfrac{12}{100}\times0.14=\$336$/yr (electric saves $769/yr). $MV_n=P(0.90)^n$; total cost = purchase − resale + energy.

(a) Total Cost if Sold After 3 Years

Gasoline: $MV_3=24{,}000(0.9)^3=\$17{,}496$; cost $=24{,}000-17{,}496+3(1{,}105)=\$9{,}819$.

Electric: $MV_3=36{,}000(0.9)^3=\$26{,}244$; cost $=36{,}000-26{,}244+3(336)=\$10{,}764$.

$$\text{Gasoline } \$9{,}819 \;<\; \text{Electric } \$10{,}764 \Rightarrow \boxed{\text{Gasoline is more economic (by }\$945)}$$

(b) Gas Price that Justifies the Electric Car (4-year resale)

Gas depreciation loss $=24{,}000-24{,}000(0.9)^4=24{,}000-15{,}746.40=\$8{,}253.60$; annual litres $=1{,}300$. Electric total $=36{,}000-36{,}000(0.9)^4+4(336)=12{,}380.40+1{,}344=\$13{,}724.40$. The electric car wins when the gasoline total reaches it:

$$8{,}253.60 + 4(1{,}300)p = 13{,}724.40 \;\Rightarrow\; 5{,}200\,p = 5{,}470.80 \;\Rightarrow\; p \approx \boxed{\$1.05/\text{L}}$$

Only if gas rises above ≈$1.05/L does the all-electric car become the better choice at a 4-year resale; at today's $0.85/L the gasoline car wins.

(c) Years of Usage that Justify the Electric Car

The electric car is justified when $g(n)<0$, where (equal depreciation rates cancel the exponential difference into one term):

$$g(n) = 12{,}000\left[1-(0.9)^n\right] - 769n$$

Evaluating: $g(10)=+126$, $g(11)=-225$. The crossover is between 10 and 11 years; interpolating:

$$n \approx 10 + \frac{126}{126+225} \approx \boxed{10.4\ \text{years}}$$

The electric car's fuel savings repay its higher purchase price only after about 10.4 years—longer than most people keep a car, so the gasoline car is the economic choice for typical ownership periods.