Would you rather purchase a used car that costs $1050 up-front and will cost $300/year to...

Would you rather purchase a used car that costs $1050 up-front and will cost $300/year to run or a used car that costs $1300 up-front and will cost $250/year to run? Assume that you will own the car for 5 years and your discount rate is 5%

Solutions

Expert Solution

Discount rate (d) = 5%

Present valeu can be calculated as R / (1 + d)n

R = Run cost in that year

n = nth year

Car cost = $1,050

Present value to run in 1st year of car = 300 / (1 + 0.05)1 = 285.71

Present value to run in 2nd year of car = 300 / (1 + 0.05)2 = 272.1

Present value to run in 3rd year of car = 300 / (1 + 0.05)3 = 259.15

Present value to run in 4th year of car = 300 / (1 + 0.05)4 = 246.81

Present value to run in 5th year of car = 300 / (1 + 0.05)5 = 235.05

Sum of all present value to run the car = 1,298.81

Total present value of purchasing this car = 1,050 + 1,298.82 = 2,348.82

Car cost = $1,300

Present value to run in 1st year of car = 250 / (1 + 0.05)1 = 238.09

Present value to run in 2nd year of car = 250 / (1 + 0.05)2 = 226.75

Present value to run in 3rd year of car = 250 / (1 + 0.05)3 = 215.95

Present value to run in 4th year of car = 250 / (1 + 0.05)4 = 205.67

Present value to run in 5th year of car = 250 / (1 + 0.05)5 = 195.88

Sum of all present value to run the car = 1,082.34

Total present value of purchasing this car = 1,300 + 1,082.34 = 2,382.34

As present value of first car is less, I will purchase car with up front cost of $1,050

Rahul Sunny answered 1 week ago

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