A new six-speed automatic transmission for automobiles offers an estimated 3% im

Question

A new six-speed automatic transmission for automobiles offers an estimated 3% improvement in fuel economy compared to traditional four speed transmissions in front-wheel drive cars. If a four-speed transmission car averages 27 miles per gallon and gasoline costs $2.50 per gallon, how much extra can a motorist pay for a fuel-efficient six-speed transmission? Assume that the car will be driven for 134,000 miles over its lifetime of 9 years. The motorist can earn 6% per year on investments. Assume miles driven each year are roughly constant. Click the icon to view the interest and annuity table for discrete compounding when the MARR is 6% per year. The motorist can pay for a fuel-efficient six-speed transmission extra $ (Round to the nearest dollar.)

Explanation / Answer

Current mileage = 27 mile per gallon

For driving 134,000 miles, fuel needed = 134,000 / 27 = 4,962.96 gallons

A 3% improvement in fuel efficiency means, new mileage = 27 miles x 0.03 = 27.81 miles per gallon

For driving 134,000 miles, fuel needed = 134,000 / 27.81 = 4,818.41 gallons

Reduction in fuel requirement = (4,962.96 - 4,818.41) = 144.55 gallons

Total Cost savings at end of year 9 = 144.55 gallons x $2.5 per gallon = $361.38

Present value of this cost saving = $361.38 / (1.06)9 = $361.38 / 1.6895

= $213.9

= $214 (nearest dollar)

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

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