Final answer:
Using the high-low method, the expected total cost for driving a truck 110,000 miles is calculated to be $26,680, with the variable and fixed costs considered.
Step-by-step explanation:
The high-low method is a technique used in cost accounting to determine variable costs and fixed costs associated with producing a good or service. In this scenario, Joy Inc. has provided two data points regarding the cost per mile at two different levels of activity (mileage).
- At 120,000 miles, the cost is 11.6 cents/mile.
- At 80,000 miles, the cost is 13.6 cents/mile.
To calculate the variable cost per mile and the fixed cost, we follow these steps:
- Calculate the variable cost per mile as the difference in cost divided by the difference in miles.
- Determine the total fixed cost by calculating the total cost at either level of activity and then subtracting the total variable cost found in step 1.
- Compute the total expected cost for 110,000 miles using the formula: Total Cost = (Variable Cost per Mile × Number of Miles) + Fixed Cost.
Calculation of the variable cost per mile:
Variable Cost per Mile = (13.6 cents - 11.6 cents) / (80,000 miles - 120,000 miles)
Variable Cost per Mile = 2 cents / -40,000 miles
Variable Cost per Mile = -0.00005 dollars per mile (meaning for each additional mile driven, the cost decreases by 0.00005 dollars)
Calculation of the fixed cost:
Fixed Cost = Total Cost at Any Activity Level - (Variable Cost per Mile × Miles at that Level)
Let's use the 120,000 miles data point:
Fixed Cost = (120,000 miles × $0.116) - (120,000 miles × -$0.00005)
Fixed Cost = $13,920
Calculation of the total expected cost for 110,000 miles:
Total Expected Cost = ($0.116 - $0.00005) × 110,000 miles + $13,920
Total Expected Cost = $12,760 + $13,920
Total Expected Cost = $26,680
The final answer is that the expected total cost for a truck being driven 110,000 miles during the year would be $26,680.