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for sutomobiles offers an estimatnd 10 traditional four-speed trunsminsion fror

ID: 2657358 • Letter: F

Question

for sutomobiles offers an estimatnd 10 traditional four-speed trunsminsion fror t in fucl economy compared to cars. Assume that the for-speed transmision e per galion and gasoline costs $2.5 per galion, on the car will be drives for 30,000 kilemeters per year years and that the lifetiame of the au is 10 a. Find the anmaal saving six-speed (3 poins) uiomebie g if the six-speed transmision is seloczed. How much extra should a motorist pay foe the skx-speed transmission eemotorist can eam 10% per year on investment? (2 peints)

Explanation / Answer

(a) Four Speed Transmission: 50 km per gallon, Price per Gallon = $ 2.5, Annual Running = 30000 km

Annual Fuel Requirement = 30000 / 50 = 600 gallon

Annual Fuel Cost = 2.5 x 600 = $ 1500

Six Speed Transmission: 10 % improvement in fuel efficiency implies that the car will run (50 x 1.1) = 55 km pr gallon, Fuel Cost = $ 2.5 per gallon and Annual Running = 30000 km

Annual Fuel Requirement = 30000 / 55 = 545.45 m

Annual Fueld Cost = 2.5 x 545.45 = $ 1363.625

Annual Fuel Cost Savings = 1500 - 1363.625 = $ 136.375

(b) Investment Earnings Rate = 10 % and Car Lifetime = 10 years

PV of Annual Fuel Cost Savings = 136.375 x (1/0.1) x [1-{1/(1.1)^(10)}] = $ 837.96

The extra cost to be paid for selecting the six speed transmission should be equal to the total present value of the expected annual fuel cost savings over the car's lifetime.