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

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. a. Find the annual saving if the six-speed transmission is selected. (3 points) b. 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)

Explanation / Answer

6.

A.

Total cost incurred per year by traditional four speed cars = (30000/50)*2.5 = $1500

So,

Annual savings using six speed system = 1500*10% = $150

Hence, annual savings using 6-speed system, will be $150.

B.

Time = 10 years

R = 10%

Extra amount to be paid is the present value of annual savings over a period of 10 years.

Present value of the savings = 150*(1-1/1.1^10)/.1

Present value of the savings = $921.69

So, extra amount to be paid is $921.69.

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