A new six-speed automatic transmission for automobiles offers an estimated 4% im

Question

A new six-speed automatic transmission for automobiles offers an estimated 4% improvement in fuel economy compared to traditional four speed transmissions in front wheel drive cars. If a four speed trans. car averages 32 miles per gallon and gasoline costs $2.50 per gallon, how much extra can a motorist pay for a fuel efficient 6 speed transmission? Assume the car will be driven for 140,000 miles over its lifetime of 12 years. The motorist can earn 5% per year on investment Assume miles driven each year are roughly constant.

I understand how to convert between the two cars but I'm confused how to factor in the investment. Explanation of that portion would be most beneficial. Thank you.

Explanation / Answer

Current mileage = 32 mile per gallon

For driving 140,000 miles, fuel needed = 140,000 / 32 = 4,375 gallons

A 4% improvement in fuel efficiency means, new mileage = 32 miles x 1.04 = 33.28 miles per gallon

For driving 140,000 miles, fuel needed = 140,000 / 33.28 = 4,206.73 gallons

Reduction in fuel requirement = (4,375 - 4,206.73) = 168.27 gallons

Total Cost savings at end of year 12 = 168.27 gallons x $2.5 per gallon = $420.68

Present value of this cost saving = $420.68 / (1.05)12

= $234.25

So, this is the maximum amount that consumer be willing to pay extra.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.