Question

Cost Behavior; High-Low Method

Speedy Parcel Service operates a fleet of delivery trucks in a large metropolitan area. A careful study by the company's cost analyst has determined that if a truck is driven 120,000 miles during a year, the average operating cost is 11 .6 cents per mile. If a truck is driven only 80,000 miles during a year, the average operating cost increases to 13.6 cents per mile.
Required:
I. Using the high-low method, estimate the variable and fixed cost elements of the annual cost of truck operation.
2. Express the variable and fixed costs in the form Y= a+ bX.
3. If a truck were driven 100,000 miles during a year, what total cost would you expect to be incurred?

Answer 1

To calculate the variable and fixed costs using the high-low method, we find the variable cost per mile based on the difference in costs between the high and low activity levels, then subtract the total variable cost from the total cost to find the fixed cost. However, with the given information, we only deduced that the costs decrease as mileage increases and cannot calculate fixed costs without the total cost at a certain activity level. Consequently, we cannot compute the expected total cost for 100,000 miles without the fixed cost.

Step-by-step explanation:

Using the high-low method, we start by calculating the variable cost per mile. This is done by taking the difference in cost between the high and low activity levels and dividing it by the difference in miles driven. With 120,000 miles driven, the cost is 0.116 dollars per mile, and for 80,000 miles driven, the cost is 0.136 dollars per mile.

The formula for variable cost per mile is: (Cost at High Activity Level - Cost at Low Activity Level) / (High Activity Level - Low Activity Level).

Variable cost per mile = (0.136 - 0.116) / (80,000 miles - 120,000 miles) = 0.02 / (-40,000) = -0.0005 dollars per mile. Since we cannot have negative variable costs, this indicates that the costs decrease as the mileage increases, which can be explained by spreading the fixed costs over more miles.

Next, we calculate the total fixed cost by subtracting the total variable cost at either activity level from the total cost at that level. Let's use the 80,000 miles level for this example. Total variable cost at this level is 80,000 miles * 0.136 dollars/mile = 10,880 dollars. To find the fixed cost, we need the total cost at this level, which we don't have, so we cannot complete this part without additional information.

To express these findings in the form Y = a + bX, where 'Y' is the total cost, 'a' is the total fixed cost (which we couldn't determine), and 'b' is the variable cost per mile. Thus, Y = a + (-0.0005)X. Without knowing the fixed cost, 'a', we cannot provide a specific formula.

Lastly, if a truck were driven 100,000 miles during a year, since we do not have the fixed cost, we cannot calculate the total expected cost accurately. We are missing the total cost information required to use the high-low method effectively.

Answer 2

Answer and Explanation:

The computation is shown below;

a. The variable and fixed cost elements is

The variable is

= (120,000 miles × 0.116) - (80,000 × 0.136) ÷ (120,000 - 80,000 miles)

= ($13,920 - $10,880) ÷ (40,000 miles)

= $0.076

Now the fixed cost is

= $13,920 - ($0.076 × 120,000)

= $4,800

b. The expression is

Y = $4,800 + $0.076X

c. The total cost is

= $4,800 + 100,000 × $.076

= $12,400