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23-CS-1 Engineering Economics · May 2016

Question 3 of 5: Gasoline versus Hybrid Car

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

Notes on this paper

National Exams — May 2016 — 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 3: Gasoline versus Hybrid 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 Fuel Costs

Gasoline: $20{,}000\ \text{km}\times\frac{6.5}{100}\times\$0.75 = \$975$/yr. Hybrid: $20{,}000\times\frac{4.5}{100}\times\$0.75 = \$675$/yr. Hybrid saves $300/yr in fuel. Resale after $n$ years: model value $\times(0.9)^n$.

(a) Net Cost After 3 Years (i = 0%)

Net cost = price − resale + total fuel. With $(0.9)^3 = 0.729$:

$$\text{Gasoline} = 20{,}000(1-0.729) + 975(3) = 5{,}420 + 2{,}925 = \$8{,}345$$
$$\text{Hybrid} = 24{,}000(1-0.729) + 675(3) = 6{,}504 + 2{,}025 = \$8{,}529$$

The gasoline model is more economic after 3 years ($8,345 < $8,529)—the hybrid's fuel savings do not yet cover its higher net purchase cost.

(b) Years of Usage to Justify the Hybrid

The hybrid's extra net cost is $4{,}000(1-0.9^{n})$ (extra price less extra resale); its fuel saving is $300n$. The hybrid is justified when the saving covers the extra cost:

$$300n \ge 4{,}000(1-0.9^{n})$$

Testing: at $n=6$, $1{,}800 < 1{,}874$ (no); at $n=7$, $2{,}100 > 2{,}087$ (yes). The break-even is about $n\approx 6.9$, so roughly 7 years of ownership justifies buying the hybrid.

(c) Gasoline Price to Justify the Hybrid Over 5 Years

Fuel used per year: gasoline 1,300 L, hybrid 900 L, so the hybrid saves 400 L/yr, i.e. $400p$ per year at price $p$. Over 5 years the extra net cost is $4{,}000(1-0.9^{5}) = 4{,}000(0.40951)=\$1{,}638$. Setting the 5-year fuel saving equal to it:

$$5(400)p = 1{,}638 \;\Rightarrow\; 2{,}000p = 1{,}638 \;\Rightarrow\; p \approx \boxed{\$0.82/\text{L}}$$

At a gasoline price of about $0.82/L or higher, the hybrid becomes economic over a 5-year ownership.