Hoi Chong Transport, Ltd., operates a fleet of delivery trucks in Singapore. The company has determined that if a truck is driven 129,000 kilometers during a year, the average operating cost is 13.7 cents per kilometer. If a truck is driven only 86,000 kilometers during a year, the average operating cost increases to 16.8 cents per kilometer. Requried:
a. Using the high-low method, estimate the variable and fixed cost elements of the annual cost of the truck operation.
b. Express the variable and fixed costs in the form Y = a + bX.

A. Variable cost per unit 0.075 per kilometer

Fixed cost $7,998

B. Y= 0.075 + 7,998X

Explanation:

A. Calculation to estimate the variable and fixed cost elements of the annual cost of the truck operation.

First step is to calculate the operating cost if the Truck is driven 129,000 kilometers during a year in which the average operating cost is 13.7 cents per kilometer

​Operating cost= 129,000 x 13.7/100

​Operating cost= $17,673

Second step is to calculate the operating cost if Truck is driven only 86,000 kilometers during a year in which the average operating cost increases to 16.8 cents per kilometer.

Operating cost = 86,000 x 16.8/100

Operating cost =$14,448

Calculation for VARIABLE COST PER UNIT using this formula

Variable cost per unit = (Highest activity cost - Lowest activity cost)/(Highest activity - Lowest activity)

Let plug in the formula

Variable cost per unit= $17,673-$14,448)/(129,000-86,000)

Variable cost per unit= 3,225/43,000

Variable cost per unit= 0.075 per kilometer

Calculation for FIXED COST using this formula

Fixed cost = Highest activity cost - Highest activity x Variable cost per kilometer

Let plug in the formula

Fixed cost= $17,673 - 129,000 x 0.075

Fixed cost= $17,673 -$9,675

Fixed cost=$7,998

Therefore the variable is 0.075 per kilometer and fixed cost elements of the annual cost of the truck operation is $7,998

B. Expression of the variable and fixed costs in the form Y = a + bX.

Y = a + bX

Y= 0.075 + 7,998X

Therefore the variable and fixed costs in the form Y = a + bX will be Y= 0.075 + 7,998X

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