Question 6 (5 Points): A new six-speed automatic transmission for automobiles of

Question

Question 6 (5 Points): A new six-speed automatic transmission for automobiles offers an estimated 10% improvement in fuel economy compared to traditional four-speed transmission front- wheel drive cars. Assume that the four-speed transmission car allows it to drive 50 kilometers per gallon and gasoline costs $2.5 per gallon, on average. Also, assume that the car will be driven for 30,000 kilometers per year and that the lifetime of the car is 10 years Find the annual saving if the six-speed transmission is selected. (3 points) How much extra should a motorist pay for the six-speed transmission automobile, if the motorist can earn 10% per year on investments? (2 points) a. b.

Explanation / Answer

(a)

For the 4-speed transmission motor car, Number of gallons of fuel per year = 30,000 / 50 = 600

Annual fuel cost = 600 x $2.5 = $1,500

For a 6-speed transmission motor car, a 10% improvement in fuel economy indicates that there will be 10% increase in mileage. So, mileage will be (50 KM per gallon x 1.1) = 55 KM per gallon.

Number of gallons of fuel per year = 30,000 / 55 = 545.45

Annual fuel cost = 545.45 x $2.5 = $1,363.64

Annual fuel saving = $1,500 - $1,363.64 = $136.36

(b)

Maximum additional amount = Present value of annual savings of fuel cost

= $136.36 x PVIFA(10%, 10) = $135.36 x 6.1446** = $837.90

**From PVIFA factor table

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