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 comapared to tradtional four speed transmissions in front wheel drive cars. If a four speed transmission car averages 26 miles per gallon and gasoline cost $2.50, how much extra can a motorist expect to pay for a fuel effiecient six speed transmission? Assume that the car will be driven 139,000 miles over its lifetime of 10 years. The motorist can earn 8% per year on investments. Assume miles driven each year are roughly constant.

Explanation / Answer

6 speed transmission

The lifetime miles= 139000

The costs incurred on fuel = 139000*2.5/26.76 (26+3%improvement)

=$12985.8

4-Speed transmission

The lifetime miles = 139000

The costs incurred on fuel = 139000*2.5/26

=$13365.4

The difference in the costs incurred = 13365.4 -12985.8 = 380 (379.6)

The return on this is 8% (if this $380 saving is invested for 10 years.) =380*(1+0.08)^(10) = $819.5

This means that the total cost savings in 6 speed transmission will save approximately 819.5+380 = $1199

$1199 is what a motorist will be ready to pay for a fuel efficient six speed transmission.

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