Hoi Chong Transport, Ltd., operates a fleet of delivery trucks in Singapore. The company has determined that if a truck is driven 126,000 kilometers during a year, the average operating cost is 13.3 cents per kilometer. If a truck is driven only 84,000 kilometers during a year, the average operating cost increases to 15.5 cents per kilometer. Required:1. Using the high-low method, estimate the variable operating cost per kilometer and the annual fixed operating cost associated with the fleet of trucks.2. Express the variable and fixed costs in the form Y = a + bX.3. If a truck were driven 105,000 kilometers during a year, what total operating cost would you expect to be incurred?

Hoi Chong Transport, Ltd.

1. Using high-low method to estimate the variable operating cost per kilometer and the annual fixed operating cost:

High point 126,000Km, cost = $16,758 (13.3 cents x 126,000)

Low point 84,000km, cost = $13,020 (15.5 cents x 84,000)

Difference 42,000km, cost = $3,738

i) Variable Cost per km = $3,738/42,000 = $0.09

ii) Fixed cost using low point = $13,020 - (84,000 x $0.09) = $5,460

2. Variable and fixed costs in the form of Y = a + bX

where Y = total costs

a = fixed cost

b = variable cost

X = kilometers driven

Y = $5,460 + $0.09X

3. Total operating cost (Y), if truck were driven 105,000

Y = $5,460 + $0.09 x 105,000 = $14,910

Explanation:

The high-low method is a technique for determining the variable and fixed elements of total cost.  The techniques uses the highest quantity with its total cost and the lowest quantity with its total cost.  The resulting cost is the variable cost.  Then the variable cost per unit is determined by dividing the cost with the quantity.

Then, the variable cost per unit is superimposed on the formula, Y = a + bX, where Y is the total cost, a is the fixed cost, b is the variable cost, and X is the quantity.  Solving for a or fixed cost, gives a = Y - bX.