Question

A new American graduate is contemplating buying a

Japanese, German, or an American car. No matter the type of car, he
plans to buy a new one at the end of 8 years.
The Japanese cars will cost $30,000 and have a fuel
usage of 23 Miles Per gallon (mpg) for the first 2 years and will
decrease by 3% per year thereafter. The repair cost will start at $700
per year, and increase by 3% per year. At the end of year 8, the
car can be sold for $5000. Insurance cost will be $700 for the
first year, increasing by 2% per year thereafter.
​A German car will cost $45,000 and have fuel usage
of 21mpg for the first 5 years, and decrease by 1% thereafter to
year 8. The repair cost will start at $1000 in year 1 and increase by
4% per year. It will have a salvage value of $7000 at the end of
year 8. Insurance cost will be $850 the first year, increasing by
2% per year thereafter.
The American car will cost $35,000 and have fuel
usage of 20mpg for the first 3 years and will decrease by 3% per
year thereafter. The repair cost will be $800 in year 1, increasing by
4% per year thereafter. Being an American, the graduate will price
the pride of owning an American car at $0.4 for every 20 miles
driven, increasing by 2% per year. Insurance costs will be $800 per
year increasing by 2.2% per year. The car can be sold for $5500 at
the end of year 8.
If the graduate anticipates driving 150000 miles by
the end of year 8 and the average interest rate is expected to
remain at 5% per year, which car is economically affordable based
on present worth analysis? Assume fuel cost will be $3 per gallon
in year 1 and increase by an average of 2% per year. Show all your
workings.​

Answer 1

The best option is to buy Japanese Car.

Step-by-step explanation:

Fuel usage per year is 150000/ 8 = 18750 miles per year

Fuel cost (year 1 -8) = $3.0, $3.06, $3.12, $3.18, $3.25, $3.312, $3.38, $3.5

Japanese Car:

Fuel usage 18750 / 23 = 815 * $3 = $2446

Fuel charges (year 1 -8) = $2445, $2494, $2623, $2758. $2900, $3050, $3207, $3372

Repair Cost (year 1 - 8) = $700, $721, $742, $764, $787, $811, $835, $860

Insurance cost (Year 1 - 8) = $700, $714, $728, $742, $757, $772, $788, $804

Present value of cost at 5% = 24674.07

Cost of car is $30,000

Total cost = $54674.07

American Car:

Cost $35,000

Fuel usage 18750/20 = 937.5 * $3 per gallon = $2812.5.

Fuel charges (year 1 -8) = $2812, $2913, $2986, $3011. $3098, $3124, $3176, $3208

Repair Cost (year 1 - 8) = $800, $894, $921, $978, $1109, $1176, $1207, $1301

Insurance cost (Year 1 - 8) = $800, $827, $876, $898, $908, $932, $954, $934

Present value of cost at 5% = 25302.18

Cost of car is $35,000

Total cost = $60302.

German Car:

Cost = $45,000

Fuel usage 18750 / 21 = 892 * $3 = $2678

Fuel charges (year 1 -8) = $2679, $2732, $2786, $2842. $2899, $2987, $3077, $3171

Repair Cost (year 1 - 8) = $1000, $1040, $1081, $1124, $1169, $1216, $1265, $1316

Insurance cost (Year 1 - 8) = $850, $867, $884, $902, $920, $938, $957, $976

Present value of cost at 5% = 27105.73

Cost of car is $45,000

Total cost = $72105.