Question

A consumer decides to perform an economic analysis to compare two different automobiles intended for use over the next 10 years. The first auto named Auto_1 averages 23 km per gallon and costs $25,000. Consumer Reports says that the time between failures is gamma with a shape parameter of 2.58 and a scale parameter of 5000 km with an average repair cost of $508. Routine servicing is required every 6000 km at a cost of $130. Trade-in value after 10 years is estimated to be $11,000. The second auto named Auto_2 averages 21 km per gallon and costs $23,000. It has a time between failure distribution that Consumer Reports says is minimum extreme value with a scale parameter of 805 and a location parameter of 9350 km. Average repair cost as advertised is $400. Routine servicing is required every 6500 km at a cost of $145. Trade-in value after 10 years is estimated to be $9500. The consumer averages 18,000 km per year and has an available investment rate of return 4.5 percent. Inflation is expected to be average 3.25% in every year over the next decade.

Questions

1) Given the cost of gasoline will be $3.0 per gallon in the first year and it will be increased year by year based on the inflation rate, which automobile should be purchased based only on the economic data provided? Provide a short analysis.

2) How is the life cycle costs comparison if the cost of gasoline averages 3.50 (inflation has been considered) a gallon and the automobile is driven 16,000 km/year?

Answer 1

Automobile A	Automobile B	Particulars
23 Km	21 Km	Average Km Per Gallon
25000 $	23000 $	Cost
508 $	400 $	Average Repairing Cost
130/6000 $	145/6500 $	Routine Servicing Cost Per Km
11000 $	9500 $	Trade in Value After 10 Yrs

Cost of Gasoline is 3 $ per gallon in the first year

1. For A Automobile, the average cost would be:

For 1 Km = [25000/23] - 508 -[130/6000] = 1086.95 - 508 - 0.021 = 578.9 = 579 $ approx.

Therefore, Total Average Cost would be 579 * 3 = 1737 $ per gallon [if the gasoline rate is 3 $ per gallon] for consumer's average @18000 km/yr

Similalry, For B Automobile, the average cost would be:

For 1 Km = [23000/21] - 400-[145/6500] = 1095.23- 400 - 0.022 = 695.2 = 695 $ approx.

The Total Average Cost would be 695 * 3 = 2085 $ per gallon [if the gasoline rate is 3 $ per gallon] for consumer's average @18000 km/yr

Comparing both A & B Automobile Costs per Gallon, The consumer should go for the lesser cost incurred by Automobile A which is 1737$ as compared to Automobile B i.e. 2085$

2. For Automobile A, the average yearly cost would be 11000/10 = 1100 $

and, average yearly cost per gallon considering the cost of gasoline at an average rate of 3.5 will be 1100*3.5 = 3850 $ for 16000 km/yr

Similarly for Automobile B, the average yearly cost would be 9500/10 = 950 $

and, average yearly cost per gallon considering the cost of gasoline at an average rate of 3.5 will be 950*3.5 = 3325 $ for 16000 km/yr

So, considering the life costs, the consumer should go for automobile B bearing cost @ 3325$ as compared to automobile A bearing cost @ 3850$