Question

Cost Behavior; High-Low Method [LO2-4, LO2-5] Hoi Chong Transport, Ltd., operates a fleet of delivery trucks in Singapore. The company has determined that if a truck is driven 105,000 kilometers during a year, the average operating cost is 11.4 cents per kilometer. If a truck is driven only 70,000 kilometers during a year, the average operating cost increases to 13.4 cents per kilometer. Required: 1. Using the high-low method, estimate the variable and fixed cost elements of the annual cost of the truck operation. 2. Express the variable and fixed costs in the form Y = a + bX. 3. If a truck were driven 80,000 kilometers during a year, what total cost would you expect to be incurred?

Answer 1

Answer:

Y=4200+0.074X

At  activity level of 80,000 kilometers total cost is $10,120

Explanation:

Variable cost=(cost at higher activity-cost at lower activity level)/(vol. at higher activity level-vol. at lower activity level)

cost at higher activity  level=105000*0.114=$11,970

cost at lower activity level=70000*$0.134=$9,380

variable cost=($11,970-$9,380)/(105,000-70,000)

                     =$0.074

The cost function is Y=a+bX

where Y is total cost

a is fixed cost

b is the variable cost

X is the volume of output at a particular level of output

by substituting variable cost at higher activity level of 105000 units

$11,970=a+($0.074*105000)

$11,970=a+$7770

a=$11,970-$7,770

a=$4,200

Y=4200+0.074X

If 80,000 kilometers were driven during the year,the total cost is computed thus:

Y=$4200+($0.074*80000)

Y=$4200+$5920

Y=$10,120