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. If a four speed transmission car averages 30 MPG and gasoline costs $4.00 per gallon, how much extra cost can a motorist pay for a fuel efficient six speed transmission? Assume that the car will be driven for 120,000 miles over its lifetime for 10 years. The motorist can earn 6% per year on investments. The motorist can pay for a fuel efficient six speed transmission extra $_________. The answer is $453.00, I just need to know how they got there...

Explanation / Answer

Total Fuel Cost when using traditional transmission = Miles Per Year / Miles Per Gallon * Per Gallon Cost

= Miles / year = 120000 / 10 = 12000 miles

So Total Fuel Cost = 12000/30 * 4 = $1600

With 6 speed , miles per gallon = 30 * (1+ 0.04) = 30* 1.04 = 31.20 MPG

So Now Revised Cost = 12000 / 31.20 * 4 = 1538.50

So, Yearly Savings in cost = 1600 - 1538.50 = $61.50 per year

So, every year we save $61.50

Hence the maximum anount that will be paid extra is the present value of all the savings where n =10 and i = 6%

So, PVIFA (n=10 , i=6%) = 7.3601

So Present Value of Cash Flows = 61.50 * 7.3601 = $ 453

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