Question

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.

Answer 1

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

Step-by-step 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