Question

Blue Star is starting a new distribution service that delivers auto parts to the service departments of auto dealerships in the local area. Blue Star has found two light-duty trucks that would do the job well, so now it needs to pick one to perform this new service. The Ford TriVan costs $28,000 to buy and uses regular unleaded gasoline, with an average fuel efficiency of 24 miles per gallon. The TriVan has an operating cost of $.20 per mile. The Honda CityVan, a hybrid truck, costs $32,000 to buy and uses regular unleaded gasoline and battery power; it gets an average of 37 miles per gallon. The CityVan has an operating cost of $.22 per mile. The distance traveled annually is estimated to be 22,000 miles, with the life of either truck expected to be 8 years. The average gas price is $4.25 per gallon.
Required:
a. Based on life cycle cost, which model truck is the best choice?
b. How many miles does Blue Star need to put on a truck for the costs to be equal?
c. What is the crossover point in years?

Answer 1

Answer:

Blue Star

a.                                   The Ford TriVan   The Honda CityVan

Total life-cycle costs          $94,368                $90,936

Based on life cycle cost, the Honda CityVan is the best choice.

b. Blue Star needs to put on the Ford TriVan 9,032 miles more for the cost to be equal with the Honda CityVan's.

c. The crossover point in years = 5 months

Step-by-step explanation:

a) Data and Calculations:

                                        The Ford TriVan   The Honda CityVan

Purchase costs                  $28,000                 $32,000

Fuel efficiency per gallon   24 miles                 37 miles

Operating cost per mile     $0.20                     $0.22

Total operating costs         $4,400                   $4,840

Estimated annual distance 22,000 miles        22,000 miles

Gallons of fuel consumed  916.7 (22,000/24) 594.6 (22,000/37)

Total cost of fuel                 $3,896                  $2,527

Fuel cost per mile              $0.18                      $0.115

Total cost per mile             $0.38                     $0.335

Expected life of truck         8 years                   8 years

Average gas price = $4.25 per gallon

Total costs:

                                        The Ford TriVan   The Honda CityVan

Annual costs:

Total operating costs         $4,400                   $4,840

Total cost of fuel                $3,896                   $2,527

Annual costs                      $8,296                   $7,367

Life cycle costs:

Annual costs for 8 years   $66,368                $58,936

Purchase costs                  $28,000                $32,000

Total life-cycle costs          $94,368                $90,936

Difference in costs between Ford TriVan and Honda CityVan = $3,432 ($94,368 - $90,936)

Miles to put on the Ford TriVan for the life cycle cost to be equal to the life cycle cost of the Honda CityVan

= Difference in costs divided by total cost per mile of the Ford TriVan

= 9,032 miles ($3,432/$0.38)

Annual distance = 22,000 miles

Monthly distance = 1,833 miles

9,032/1,833 = 4.93 months or 5 months approximately