Crossover Point Given the data in Problem S5.15 and an alternative hybrid vehicl

Question

Crossover Point

Given the data in Problem S5.15 and an alternative hybrid vehicle with the specifications shown below: a) What is the crossover point in miles? b) Which vehicle is has the lowest cost until the crossover point is reached? VEHICLE PURCHASE COST VEHICLE OPERATING COST PER MILE USEFUL UFE OF VEHICLE MILES PER YEAR MILES PER GALLON AVERAGE FUEL PRICE PER GALLON $29,000 0.08 10 years 18,000 40 2.55 (Reference Problem S5.15) Hartley Auto Supply delivers parts to area auto service centers and is replacing its fleet of delivery vehicles. What is the total vehicle life-cycle cost of this gasoline engine truck given the information provided in the following table? VEHICLE PURCHASE COST VEHICLE OPERATING COST PER MILE USEFUL LUIFE OF VEHICLE MILES PER YEAR MILES PER GALLON AVERAGE FUEL PRICE PER GALLON $25,000 $0.13 10 years 18,000 25 $2.55

Explanation / Answer

Lets assume the crossover point in miles = x

Total life cycle cost = puchase cost + fuel cost + operating cost

Truck 1:

puchase cost = $29000

fuel cost = miles driven*price per gallon/ miles per gallon

= x*2.55/40

operating cost = cost per mile*miles driven = 0.08*x

Truck2:

Purchase cost = 25000

fuel cost = x*2.55/25

operating cost = 0.13*x

for crossover point the total cost has to be equal for both:

29000 + 2.55/40 x + 0.08x = 25000 + 2.55/25 x + 0.13x

29000-25000 = 0.13x-0.08x + 2.55/25 x - 2.55/40 x

4000 = 0.05x + 0.102x - 0.06375x

4000 = 0.08825x

x = 45325.8 miles

Before the cross over point the truck2 had lesser costs since its purchase cost was less. Fuel cost is less for truck1 since it gives higher mileage per gallon and also operating costs for truck1 is less. Hence overall truck1 will be cheaper but before crossover point the truck2 is cheaper.

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