The following data is used for questions 21 and 22 and detail the life cycle costs for 2 different vehicles: Vehicle 1 Vehicle Purchase Cost $22,000 Vehicle Operating Cost per Mile $0.15 Useful Life of Vehicle 10 years Miles per Year 20,000 Miles per Gallon 25 Average Fuel Price per Gallon $2.25 Vehicle 2 Vehicle Purchase Cost $35,000 Vehicle Operating Cost per Mile $0.08 Useful Life of Vehicle 10 years Miles per Year 20,000 Miles per Gallon 45 Average Fuel Price per Gallon $2.25 What is the breakeven (or crossover point), in miles, for the two vehicles? Round off your answer to the nearest whole mile.

The breakeven (or crossover point), in miles, for the two vehicles is 118,182 miles

Explanation:

In order to calculate the breakeven (or crossover point), in miles, for the two vehicles we would have to use the following formula:

Break-even point = Difference in cost of vehicle / Difference in Variable cost per mile

Hence, we have to calculate the Difference in cost of vehicle and the Difference in Variable cost per mile .

Difference in cost of vehicle=$35,000 - $22,000 = $13,000

Difference in Variable cost per mile :

We have that the Fuel price per gallon for vehicle 1 and vehicle 2 is 2.25,

and the miles per gallon are 25 and 45 respectly, hence the average fuel cost per mile is for vehcile 1=2.25/25=0.09 and for vehichle 2=2.25/45=0.05.

We also have to add the operating cost per mile, hence, if for vehicle 1 is 0.15 and for vehichle 2 is 0.08, therefore the Total variable cost per mile for vehicle 1=0.09+0.15=0.24 and for vehicle 2=0.05+0.08=0.13

Therefore, The  Difference in Variable cost per mile = 0.24-0.13 = 0.11 per mile

Therefore, now we can calculte the Break-even point as follows:

Break-even point =13,000 / 0.11 per mile = 118,182 miles

The breakeven (or crossover point), in miles, for the two vehicles is 118,182 miles  

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